Cellular Dosimetry of 111In Using Monte Carlo N-Particle Computer Code
Monte Carlo Portal Dosimetry - Mary Chin · 2011-05-14 · downloaded from Monte Carlo Portal...
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rgMonte Carlo Portal Dosimetry
Pik Wai CHIN
A thesis presented to the University of Wales in partial fulfilment of the requirementsfor the degree of Doctor of Philosophy
c© 2005
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This work has not previously been accepted in substance for any degree and is notbeing concurrently submitted in candidature for any degree.
Signed ................................ (candidate)
Date ...................................
STATEMENT 1
This thesis is the result of my own investigations, except where otherwise stated.Other sources are acknowledged by footnotes giving explicit references. A bibliogra-phy is appended.
Signed ................................ (candidate)
Date ...................................
STATEMENT 2
I hereby give consent for my thesis, if accepted, to be available for photocopying andfor inter-library loan, and for the title and summary to be made available to outsideorganisations.
Signed ................................ (candidate)
Date ...................................
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spring summer autumn winter walk three rounds, read radiance of life, write overflowing colours of light
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Contents
Acknowledgments x
List of Tables xi
List of Figures xvi
Abstract xvii
1 INTRODUCTION 2
1.1 Radiotherapy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Imaging During Radiotherapy . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Monte Carlo Simulations . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4 Grid Computing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.5 Objective & Context . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.6 Thesis Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2 ELECTRONIC PORTAL IMAGING 17
2.1 Imager Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Megavoltage Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
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rg2.3 The SLIC and the a-Si Technologies . . . . . . . . . . . . . . . . . . . 22
3 MONTE CARLO RADIATION TRANSPORT 27
3.1 Analog and Non-analog Simulation . . . . . . . . . . . . . . . . . . . 27
3.2 Why Monte Carlo? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3 Choice of Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.4 EGSnrc, BEAMnrc and DOSXYZnrc . . . . . . . . . . . . . . . . . . 33
4 SIMULATION OF LINAC SOURCES 36
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2 Materials & Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.2.1 Migration from BEAM00 to BEAMnrc . . . . . . . . . . . . . 40
4.2.2 Selection of Transport Options . . . . . . . . . . . . . . . . . . 40
4.2.3 Fine-tuning the Linac Model . . . . . . . . . . . . . . . . . . . 42
4.2.4 Modelling Varying Field Sizes . . . . . . . . . . . . . . . . . . 43
4.2.5 Use of Phase Space Particles . . . . . . . . . . . . . . . . . . . 44
4.3 Results & Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.3.1 Migration from BEAM00 to BEAMnrc . . . . . . . . . . . . . 48
4.3.2 Selection of Transport Options . . . . . . . . . . . . . . . . . . 49
4.3.3 Fine-tuning the Linac Model . . . . . . . . . . . . . . . . . . . 51
4.3.4 Modelling Varying Field Sizes . . . . . . . . . . . . . . . . . . 51
4.3.5 Use of Phase Space Particles . . . . . . . . . . . . . . . . . . . 52
4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
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rg5 A MONTE CARLO SOLUTION 64
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.2.1 Calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.2.1.1 Image Calibration . . . . . . . . . . . . . . . . . . . 67
5.2.1.2 Grayscale-to-dose Calibration . . . . . . . . . . . . . 68
5.2.1.3 Off-axis Calibration . . . . . . . . . . . . . . . . . . 69
5.2.2 Phantom Packaging Using TWIZ&GLU . . . . . . . . . . . . 70
5.2.3 Demonstrations . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.3 Results & Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.3.1 Calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.3.1.1 Image Calibration . . . . . . . . . . . . . . . . . . . 76
5.3.1.2 Grayscale-to-dose Calibration . . . . . . . . . . . . . 77
5.3.1.3 Off-axis Calibration . . . . . . . . . . . . . . . . . . 78
5.3.2 Phantom Packaging Using TWIZ&GLU . . . . . . . . . . . . 79
5.3.3 Demonstrations . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
6 OPTIMISATION OF MONTE CARLO SIMULATIONS 88
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 90
6.2.1 Radiation Transport Studies . . . . . . . . . . . . . . . . . . . 90
6.2.2 Design of Simplified EPID Models . . . . . . . . . . . . . . . . 91
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rg6.2.2.1 A Simplified a-Si EPID Model . . . . . . . . . . . . . 93
6.2.2.2 A Simplified SLIC EPID Model . . . . . . . . . . . . 93
6.2.3 Selection of Transport Options . . . . . . . . . . . . . . . . . . 94
6.2.4 Comparison with Other Techniques . . . . . . . . . . . . . . . 96
6.3 Results & Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.3.1 Radiation Transport Studies . . . . . . . . . . . . . . . . . . . 97
6.3.1.1 The a-Si . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.3.1.2 The SLIC . . . . . . . . . . . . . . . . . . . . . . . . 101
6.3.2 Design of Simplified EPID Models . . . . . . . . . . . . . . . . 105
6.3.3 Selection of Transport Options . . . . . . . . . . . . . . . . . . 113
6.3.4 Comparison with Other Techniques . . . . . . . . . . . . . . . 114
6.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
7 PRACTICAL ASPECTS OF IMAGE ACQUISITION 120
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7.2 Materials & Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7.2.1 The SLIC: Variation with Gantry Angles . . . . . . . . . . . . 122
7.2.1.1 Angular Dependence of Images . . . . . . . . . . . . 125
7.2.1.2 Backscatter from Surroundings . . . . . . . . . . . . 126
7.2.1.3 Reproducibility . . . . . . . . . . . . . . . . . . . . . 127
7.2.1.4 Angular Correction Function . . . . . . . . . . . . . 127
7.2.1.5 Comparison with Existing Techniques . . . . . . . . 129
7.2.1.6 Application of the New Technique . . . . . . . . . . 130
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rg7.2.2 The a-Si: an Artefact in the IMRT Acquisition Mode . . . . . 131
7.2.3 The a-Si: Variation with Gantry Angles . . . . . . . . . . . . 132
7.2.4 Ideas for IMRT Verification . . . . . . . . . . . . . . . . . . . 132
7.2.4.1 An Alternative Imaging Sequence . . . . . . . . . . . 132
7.2.4.2 Rethinking Ghosts . . . . . . . . . . . . . . . . . . . 133
7.3 Results & Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
7.3.1 The SLIC: Variation with Gantry Angles . . . . . . . . . . . . 134
7.3.1.1 Angular Dependence of Images . . . . . . . . . . . . 134
7.3.1.2 Backscatter from Surroundings . . . . . . . . . . . . 135
7.3.1.3 Reproducibility . . . . . . . . . . . . . . . . . . . . . 136
7.3.1.4 Angular Correction Function . . . . . . . . . . . . . 136
7.3.1.5 Comparison with Existing Techniques . . . . . . . . 137
7.3.1.6 Application of the New Technique . . . . . . . . . . 138
7.3.2 The a-Si: an Artefact in the IMRT Acquisition Mode . . . . . 138
7.3.3 The a-Si: Variation with Gantry Angles . . . . . . . . . . . . 140
7.3.4 Ideas for IMRT Verification . . . . . . . . . . . . . . . . . . . 141
7.3.4.1 An Alternative Imaging Sequence . . . . . . . . . . . 141
7.3.4.2 Rethinking Ghosts . . . . . . . . . . . . . . . . . . . 144
7.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
8 HIGH THROUGHPUT COMPUTING 149
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
8.2 Materials & Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
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rg8.2.1 Four Levels of Implementation . . . . . . . . . . . . . . . . . . 151
8.2.2 Simulations on Multiple Platforms . . . . . . . . . . . . . . . 152
8.2.3 Planning of Simulations . . . . . . . . . . . . . . . . . . . . . 153
8.2.4 Simulations without Pre-installation . . . . . . . . . . . . . . 153
8.3 Results & Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
8.3.1 Four Levels of Implementation . . . . . . . . . . . . . . . . . . 154
8.3.2 Simulations on Multiple Platforms . . . . . . . . . . . . . . . 156
8.3.3 Planning of Simulations . . . . . . . . . . . . . . . . . . . . . 157
8.3.4 Simulations without Pre-installation . . . . . . . . . . . . . . 157
8.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
9 CONCLUSIONS 160
9.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
9.2 Further Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
A DISSEMINATION OF WORK 177
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rgACKNOWLEDGMENTS
I thank
- Cancer Research Wales and Yr Ysgol Uwchradd Tregaron, for funding.
- Geraint Lewis and Cyril Smith, for the incredible opportunities.
- Emiliano Spezi, for the tradition of excellence.
- Jeffrey Siebers, for co-supervising part of the work (Chapter 6).
- Paul Keall et al. at VCU and Phil Evans et al. at ICR/RMH, for imagingfacilities and helpful discussion.
- Frank Verhaegen and Amanda Barry, for reviewing the thesis.
- Rebecca Cufflin, for proof-reading the thesis.
- Jonathan Giddy, for facilitating High Throughput Computing services.
- colleagues at Velindre Cancer Centre, for friendship and tremendous support.
- Richard Jarvis, for assistance with image acquisition.
- Mel Jones et al., for making the phantoms.
- Andrew Edwards, for fixing the bike.
- colleagues in the scientific community far and near, for encouragement.
- housekeepers and porters at Neuadd Meirionnydd, for laughter.
- Sr Hermine, for being an inspiration still.
- Dato’ Dr Sivananthan and the late Dato’ Dr Pathmanathan, for medical carewhen I was tiny.
- physics, for 16 years of fascination.
- Brecon Beacons, for your contours of beauty.
- and the ponies, for the rhythm.
- friends and family 7000 miles away, for blessings.
- Sayang, for sayang.
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List of Tables
1.1 Technologies for digital radiotherapy imaging . . . . . . . . . . . . . . 7
1.2 Clinical applications of EPIDs . . . . . . . . . . . . . . . . . . . . . . 13
2.1 Kilovoltage versus megavoltage imaging . . . . . . . . . . . . . . . . . 22
4.1 Description of simulations performed in Chapter 4 . . . . . . . . . . . 39
4.2 Configurations for BEAMnrc simulation of linac sources . . . . . . . . 42
9.1 Original contributions reported in this thesis . . . . . . . . . . . . . . 161
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List of Figures
1.1 How radiotherapy works . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 The concept of intensity modulated radiation therapy (IMRT) . . . . 4
1.3 A linac mounted with an EPID . . . . . . . . . . . . . . . . . . . . . 6
1.4 How Monte Carlo simulations work . . . . . . . . . . . . . . . . . . . 9
1.5 Distributed processing in context . . . . . . . . . . . . . . . . . . . . 11
1.6 Thesis structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1 Image formation in x-ray transmission radiography . . . . . . . . . . 18
2.2 Interplay between contrast, spatial resolution and noise . . . . . . . . 19
2.3 A transmission imaging system . . . . . . . . . . . . . . . . . . . . . 21
2.4 Kilovoltage versus megavoltage imaging . . . . . . . . . . . . . . . . . 23
2.5 Contrast: bone versus air . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.6 Schematic of a generic portal imaging cassette . . . . . . . . . . . . . 25
3.1 Logic in a typical analog transport . . . . . . . . . . . . . . . . . . . 28
3.2 Condensed history for charged particle transport . . . . . . . . . . . . 29
3.3 Logic in electron transport . . . . . . . . . . . . . . . . . . . . . . . . 30
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rg4.1 BEAMnrc simulation of a linac . . . . . . . . . . . . . . . . . . . . . 40
4.2 Voxel geometry used for tallying dose deposition in a water tank . . . 44
4.3 Schematic diagram of normalisation procedure . . . . . . . . . . . . . 45
4.4 BEAM00 vs. BEAMnrc: fluence of phase space particles . . . . . . . 49
4.5 Energy fluence and energy spectrum of phase space particles . . . . . 50
4.6 Influence of incident electron energy on depth dose . . . . . . . . . . 51
4.7 Influence of radius of electron source on radiation profile . . . . . . . 52
4.8 Dose profiles in a water tank for a 2 cm × 2 cm beam . . . . . . . . . 53
4.9 Dose profiles in a water tank for a 5 cm × 5 cm beam . . . . . . . . . 54
4.10 Dose profiles in a water tank for a 10 cm × 10 cm beam . . . . . . . 55
4.11 Dose profiles in a water tank for a 15 cm × 15 cm beam . . . . . . . 56
4.12 Dose profiles in a water tank for a 20 cm × 20 cm beam . . . . . . . 57
4.13 Dose profiles in a water tank for a 25 cm × 25 cm beam . . . . . . . 58
4.14 Tally and uncertainty as a function of number of recycles . . . . . . . 59
4.15 Tally and uncertainty as a function of number of recycles and number
of phase space particles . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.16 Tally and uncertainty as a function of number of recycles, using regen-
erated phase space particles . . . . . . . . . . . . . . . . . . . . . . . 63
5.1 A MC verification framework . . . . . . . . . . . . . . . . . . . . . . 66
5.2 Defining a patient/phantom dataset and an imager on a common rec-
tilinear grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
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rg5.3 The task of modelling a phantom-imager geometry for irradiation at
gantry angle of θ◦ and the operation of TWIZ&GLU . . . . . . . . . 72
5.4 Rotation of a straight-sided square . . . . . . . . . . . . . . . . . . . 73
5.5 Identical phantoms generated using BEAMnrc and TWIZ&GLU . . . 74
5.6 A solid water phantom with an air gap at the centre . . . . . . . . . . 75
5.7 Cumulative histograms for image uniformity . . . . . . . . . . . . . . 76
5.8 Grayscale-to-dose calibration . . . . . . . . . . . . . . . . . . . . . . . 77
5.9 Off-axis calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.10 Profiles of cubes irradiated at gantry angle of 20◦ . . . . . . . . . . . 80
5.11 Profiles of a solid water phantom embedded with an air gap . . . . . 81
5.12 Irradiation of a homogeneous phantom at varying field sizes . . . . . 83
5.13 Irradiation of an inhomogeneous phantom at varying air gap distances 84
5.14 Irradiation of an inhomogeneous phantom at varying gantry angles . 85
6.1 Event count in each layer of the a-Si EPID . . . . . . . . . . . . . . . 98
6.2 Energy deposition in each layer of the a-Si EPID . . . . . . . . . . . . 99
6.3 Energy deposition in the a-Si EPID by backscattered particles . . . . 101
6.4 Event count in each layer of the SLIC EPID . . . . . . . . . . . . . . 102
6.5 Energy deposition in each layer of the SLIC EPID . . . . . . . . . . . 103
6.6 Energy deposition in the SLIC EPID by backscattered particles . . . 105
6.7 a-Si models A versus B . . . . . . . . . . . . . . . . . . . . . . . . . . 107
6.8 a-Si models A versus C . . . . . . . . . . . . . . . . . . . . . . . . . . 108
6.9 Full SLIC model versus the simplified SLIC model . . . . . . . . . . . 109
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rg6.10 RMS of differences between simplified models and full EPID models . 110
6.11 Effects of transport options on the SLIC EPID . . . . . . . . . . . . . 111
6.12 Effects of transport options on the a-Si EPID . . . . . . . . . . . . . 112
6.13 a-Si EPID versus water-slab EPID . . . . . . . . . . . . . . . . . . . 115
6.14 SLIC EPID versus water-slab EPID . . . . . . . . . . . . . . . . . . . 116
6.15 RMS of differences between water-slab and full EPID models . . . . . 117
7.1 Images before and after angular correction . . . . . . . . . . . . . . . 124
7.2 A portal image acquired at non-zero gantry angle . . . . . . . . . . . 125
7.3 The standard and the IMRT image acquisition modes . . . . . . . . . 131
7.4 Variation of Cγ with gantry angle . . . . . . . . . . . . . . . . . . . . 135
7.5 Reproducibility of images . . . . . . . . . . . . . . . . . . . . . . . . 136
7.6 The sinusoidal modulation technique versus existing techniques . . . . 137
7.7 RMS of the difference between pixels from opposing sides of profile . 138
7.8 An artefact in the IMRT mode on the aS500. . . . . . . . . . . . . . 139
7.9 An a-Si portal image acquired at gantry angle 180◦ . . . . . . . . . . 142
7.10 Proposed imaging sequence for verifying a step-and-shoot beam . . . 143
7.11 Profiles from a-Si portal images: with and without ghosting . . . . . 144
7.12 Series of images acquired on a SLIC EPID during a step-and-shoot
IMRT beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
7.13 An image acquired on a SLIC EPID during transition from a segment
to the next . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
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rg7.14 Row-by-row scanning makes it possible to reconstruct each row as a
function of time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
8.1 A multi-staged simulation on the WeSC . . . . . . . . . . . . . . . . . 158
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rgABSTRACT
This project developed a solution for verifying external photon beam radiotherapy.The solution is based on a calibration chain for deriving portal dose maps from ac-quired portal images, and a calculation framework for predicting portal dose maps.Quantitative comparison between acquired and predicted portal dose maps accom-plishes both geometric (patient positioning with respect to the beam) and dosi-metric (2D fluence distribution of the beam) verifications. A disagreement wouldindicate that beam delivery had not been according to plan. The solution addressesthe clinical need for verifying radiotherapy both pre-treatment (without patient inthe beam) and on-treatment (with patient in the beam). Medical linear acceleratorsmounted with electronic portal imaging devices (EPIDs) were used to acquire portalimages. Two types of EPIDs were investigated: the amorphous silicon (a-Si) and thescanning liquid ion chamber (SLIC). The EGSnrc family of Monte Carlo codes wereused to predict portal dose maps by computer simulation of radiation transport inthe beam-phantom-EPID configuration. Monte Carlo simulations have been imple-mented on several levels of High Throughput Computing (HTC), including the Grid,to reduce computation time. The solution has been tested across the entire clinicalrange of gantry angle, beam size (5 cm × 5 cm to 20 cm × 20 cm), beam-patient andpatient-EPID separations (4 cm to 38 cm). In these tests of known beam-phantom-EPID configurations, agreement between acquired and predicted portal dose profileswas consistently within 2% of the central axis value. This Monte Carlo portal dosime-try solution therefore achieved combined versatility, accuracy and speed not readilyachievable by other techniques.
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Monte Carlo Portal Dosimetry
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Chapter 1
INTRODUCTION
Radiation physics is around us and in many ways, for us. It underlies microwave ovens,
smoke detectors, airport luggage scanners and nuclear power plants. In medicine,
radiation physics has been applied for medical diagnosis and therapy, tissue analysis
and equipment sterilisation.
In therapeutic applications, radiation may be administered in a variety of ways
e.g. accelerator-generated radiation particles (external beam radiotherapy), sealed
(brachytherapy) and unsealed (nuclear medicine) radionuclides. Today, most radio-
therapy clinics around the world routinely treat cancer patients using photons and
electrons generated by linear accelerators (linacs), which have been around since
the early 1950s [Greene and Williams 1997]. Alternative particles [Brahme 2004, Li
et al. 2004, Suortti and Thomlinson 2003, Moch et al. 2002, Burmeister et al. 2003,
Jakel et al. 2003] and recent technologies such as state-of-the-art helical tomotherapy∗
[Mackie et al. 1993, Jeraj et al. 2004] are not widely available. This thesis focuses on
linac-generated photon beams.
∗Tomotherapy is based on a linac mounted on a CT-like ring, in which the beam rotates aroundthe patient to deliver “slice therapy”.
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CHAPTER 1. INTRODUCTION 3
1.1 Radiotherapy
Figure 1.1 illustrates how photon beam radiotherapy works. Carefully controlled, the
destructive power of radiation is invoked to achieve biological damage to cancerous
cells. Photons enter the patient’s body and interact with body tissues, generat-
ing showers of secondary photons and charged particles (to be discussed in Chapter
3). Energy is deposited along the tracks of these charged particles. This gives rise
to highly reactive chemical species which cause DNA damage by impairing cellular
functions for progeny production [Johns and Cunningham 1983].
PARTICLESEXIT LINAC
PARTICLESENTER BODY
BIOLOGICAL DAMAGE
ENERGY DEPOSITION
CHEMICAL CHANGES
PHYSICAL PROCESSES
Figure 1.1: How radiotherapy works: from physical processes (photon tracks in yellow,electron tracks in blue) and energy deposition (isodoses connect points of equal dose depo-sition) in targeted body tissues to chemical changes, and on to biological damage. Imageon the right courtesy of E. Spezi.
To improve external beam radiotherapy, continuous research interests have been
to shape the beam conformally to the target volume and at the same time avoid the
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CHAPTER 1. INTRODUCTION 4
tissues outside the target volume, particularly radio-sensitive organs. Traditionally,
beam shapes were regular (e.g. rectangular) and the dose distribution uniform. More
recently, conformal beam-shaping and intensity modulation have been implemented
in many clinics alongside the installation of multileaf collimators (MLC) to enable
irregularly-shaped beam collimation [Webb 1997, Kutcher et al. 1995]. Such complex
treatments typically require many contributing beamlets of irregular shapes and non-
uniform dose distribution, aimed from different angles at the patient (Figure 1.2).
Associated with complex radiation treatments is an increase in the degrees of free-
dom in various beam-defining parameters. Therefore, stringent verification is crucial
[Shalev 1995].
Figure 1.2: The concept of intensity modulated radiation therapy (IMRT). Contributingbeamlets are shown with corresponding intensity distributions. Image reproduced fromwww.mayfieldclinic.com.
Pre-treatment verification guards against errors in treatment planning, dose com-
putation, and transfer of parameters to the treatment machine. A thorough pre-
treatment verification exercise, however, does not eliminate the need for on-treatment
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CHAPTER 1. INTRODUCTION 5
verification. This is because it is impossible to ascertain linac performance ahead of
time∗ [Mayles et al. 1999], and it is difficult in practice to reproduce patient posi-
tioning perfectly with respect to the beam. Although unable to prevent an error,
on-treatment verification provides the only knowledge of the radiation actually deliv-
ered to the patient. In the event of an error being detected, prompt correction can
usually compensate for the inaccuracy in the course of a fractionated therapy, where
dose is delivered to the patient over a series of treatment sessions.
Diode arrays and thermoluminescent dosimeters (TLDs) are conventionally used
for treatment verification [Khan 1994, Williams and Thwaites 2000, Letourneau et al.
2004]. However, since they are usually placed on the patient’s skin surface, dose
verification is usually limited to a number of superficial points. 2D, 3D and 4D†
verification, whether pre-treatment or on-treatment, is made possible by capturing
images during radiotherapy.
1.2 Imaging During Radiotherapy
The purpose of capturing images during radiotherapy is not for diagnostic investiga-
tion, but rather to:
- detect and rectify machine and operator errors;
- detect and rectify day-to-day positional variations of the patient;
∗E.g. a 100% overdose has been reported as due to the failure of a timer inter-face card, causing lack of beam hold during MLC motion. A database containing reportsof adverse events is available at the United States Food and Drug Administration websitewww.accessdata.fda.gov/scripts/cdrh/cfdocs/cfMAUDE/search.cfm.
†The 4th dimension accounts for intra-fractional temporal changes such as respiratory motion.
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CHAPTER 1. INTRODUCTION 6
EPID
Figure 1.3: A linac mounted with a retractable electronic portal imaging device (EPID).Image adapted from www.varian.com.
- account for inter-fractional and intra-fractional variations in the patient’s anato-
my such as respiratory motion and changes in bowel filling.
Early efforts at capturing images during treatment were reported by Nielsen and
Jensen [1942] for an oesophageal treatment. A stationary photon beam was directed
towards the patient. The exit rays hit a fluorescent screen. By viewing the screen
through a lead glass window, beam positioning was corrected remotely during treat-
ment delivery.
Image capture during therapy had been primarily film-based despite various defi-
ciencies such as delay in film development, low contrast, narrow film latitude∗, noise
associated with film granularity, batch-to-batch inconsistencies and susceptibility to
under- and over-exposures. Digital, non-film technology – the electronic portal imag-
ing device (EPID) – began in the 1980s [Boyer et al. 1992, Munro 1995, Herman et al.
∗The film latitude is the possible range of exposures characterised by the film’s characteristiccurve.
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CHAPTER 1. INTRODUCTION 7
2001, Antonuk 2002]. EPIDs provide 2D transmission images by capturing images on
a plane at the exit side of the patient (Figure 1.3). Apart from real-time operation,
digital systems offer better image processing (e.g. windowing, histogram equalisation
to improve contrast), display (e.g. registration) and storage. Newer approaches aim
for 3D and even 4D imaging by integrating various imaging modalities with the linac.
Table 1.1 summarises existing and developing technologies used for digital imaging
during radiotherapy.
Table 1.1: Technologies for digital radiotherapy imaging.Technology References Clinical Implementationcamera-based EPID Partridge et al. [1999], Pang
and Rowlands [2000]Siemensa BeamView, Elektab
SRI100scanning liquid ionchamber (SLIC)EPID
van Herk and Meertens[1988], van Herk [1991],Eberle et al. [2003]
Varianc PortalVision Mk Iand II
amorphous silicon(a-Si) EPID
Antonuk et al. [1996, 1997],Munro and Bouius [1998]
Varian PortalVision aS500and aS1000, Elekta iViewGT
linacs integratedwith cone-beam CT
van Herk et al. [2004], Jaf-fray et al. [2002], Jaffray[2004]
under study at NetherlandsCancer Institute and PrincessMargaret Hospital
linacs integratedwith CT-on-rails
Dong et al. [2004] under study at M. D. Ander-son Cancer Centre
linacs integratedwith MR
Raaymakers et al. [2004] under study at University ofUtrecht
linacs integratedwith ultrasound
as reported by van Herket al. [2004]
under study in Grenoble
aSiemens Medical Solutions. The website is at www.medical.siemens.com.bElekta Radiation Oncology Solutions. The website is at www.elekta.com.cVarian Medical Systems. The website is at www.varian.com.
Of particular interest in this thesis are the scanning liquid ionisation chamber
(SLIC) and the amorphous silicon (a-Si) EPIDs, which will be discussed in detail in
Chapter 2.
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CHAPTER 1. INTRODUCTION 8
1.3 Monte Carlo Simulations
The term Monte Carlo (MC) was coined by von Neumann in the 1940s [Nahum 1988]
to designate a class of numerical methods based on random numbers. Thus named
because it is the computer simulation∗ of radiation events by “spinning the wheel of
chance” or “throwing the dice”. Thus designed because events in the birth, life and
death of each radiation particle are by nature stochastic.
The contribution of MC simulations towards precise and accurate radiotherapy
is not new. MC-derived stopping-power-ratios significantly improved absolute de-
termination of absorbed dose to water using air-kerma calibrated ionisation cham-
bers [Andreo 1988]. To varying extents, MC radiation transport is the foundation
for many conventional, kernel-based dose calculations e.g. convolution/superposition
techniques [Ahnesjo and Aspradakis 1999]. With increasing demands of complex
radiotherapy modalities (Section 1.1), however, restricting MC simulations to a one-
off kernel-generation stage is no longer adequate. Interest is therefore growing for
implementing case-by-case MC simulations in the clinic.
Details of MC simulations will be given in Chapter 3. An overview here will
suffice. Figure 1.4 outlines the working of a MC simulation. The MC simulation code
(commonly called MC engine) reads in the desired source (e.g. particle type, energy,
direction and position), geometry (e.g. coordinates of orthogonal planes), transport
parameters (e.g. threshold energy below which tracks should be terminated) and
∗Throughout this thesis, simulation refers to MC simulation of radiation transport in the com-puting environment. It should not be confused with the simulation procedure which is part ofradiotherapy planning, where the patient is positioned as would be during treatment and is scannedusing a simulator machine.
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CHAPTER 1. INTRODUCTION 9
STATISTICAL ANALYSIS
CROSS−SECTION
LOOKUP / CALCULATION GENERATION
RANDOM NUMBER
OUTPUT
USER INPUTS:
GEOMETRY, SOURCE, TRANSPORT PARAMETERS, TALLY SPECIFICATIONS
MONTE CARLO ENGINE
TRANSPORT ALGORITHMSnext history
Figure 1.4: How MC simulations work.
tally∗ specification (e.g. dose in a specified region). Using a pseudorandom number†,
a particle is created. During the lifetime of this particle, secondary particles may
be created, resulting in a shower or a cascade of particles. Each particle track is
simulated based on interaction physics. A history finishes when the particle and all
its secondaries
- travel beyond the “universe” of the specified geometry; or
- lose so much energy that the remaining energy falls below a user-defined thresh-
old, determined such that eventual contribution of the particle to the tally is
expected to be negligible.
∗A tally is the quantitative outcome the user requests of the simulation.†In a true random sequence, it would be theoretically impossible to predict the next digit based
on the digits up to a given point. Numerical methods normally use digits generated deterministicallyusing algorithms – which means that the next digit can be predicted. Hence the term pseudorandom,which is effectively random so long as repetition does not occur within the lifetime of the application.
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CHAPTER 1. INTRODUCTION 10
Computation then moves on to the next history by creating and tracking another
particle, and the subsequent shower, using a different pseudorandom number. The
total number of histories is decided by the user according to statistical requirement.
The higher the number of histories, the longer the run time. Each history serves
as an independent sample contributing towards the simulation result or tally, which
is a statistical estimate. When the number of histories simulated is large enough,
quantitative information on the transport process may be obtained by averaging over
the histories.
Serial computation of millions of histories, one after another, requires long run
times∗. This is clinically impractical. Hence the delay in implementing MC simula-
tions in radiotherapy clinics.
Parallel computation of histories by distributing the computation over many pro-
cessors, all working simultaneously, shortens run times. In pursuit of shorter run
times, cluster-computing is gaining popularity, to the extent of becoming a necessity,
within the MC community [Love et al. 2000, Seco et al. 2005]. The next section goes
beyond clusters.
1.4 Grid Computing
The Grid is an emerging infrastructure expected to transform our society, particularly
in science and industry [Foster and Kesselman 2003]. The idea is to provide computing
resources in a way analogous to the electric power grid – pervasive supply on demand.
∗Weeks, for a typical clinical case, on an average computer of today.
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CHAPTER 1. INTRODUCTION 11
NODE
CLUSTER
GRID
DISTRIBUTED
LESS SECURE
LESS CENTRALISED
MORE STORAGE CAPACITY
MORE PROCESSING POWER
SINGLE
Figure 1.5: Distributed processing in context: single node, cluster, distributed and Gridcomputing.
Figure 1.5 puts into context the various levels in distributed processing. Cluster
computing is simpler because it usually adopts a common operating system; ownership
is typically single and local, allowing good control; workload is normally predictable,
allowing easy coordination. Grid resources, on the other hand, have heterogeneous
operating systems managed by service providers; interfacing is complex; resources are
abundant; security issues require care.
By combining large-scale resource sharing – computers, networks, data, sensors
and people – Grid computing is expected to allow new modes of scientific enquiry, pre-
viously not feasible, to emerge. It is envisaged to be the problem-solving environment
especially for simulation-based and data-intensive sciences.
That is the outlook. Software infrastructure for the Grid is under rigorous devel-
opment towards realising a persistent, coherent, self-regulating plug-and-play utility
service. Whereas the Grid has been extensively deployed in some experimental and
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CHAPTER 1. INTRODUCTION 12
observational areas of physics, medical physics applications such as MC calculations
for radiotherapy are only now being initiated into the Grid [Chin et al. 2004a]. This
thesis presents some initial contributions, results of a joint effort with the Welsh
e-Science∗ Centre.
1.5 Objective & Context
The objective of this thesis is to develop a clinically practical MC calculation solution
for predicting “virtual” portal images for dosimetric verification of external photon
beam radiotherapy.
Portal images have been primarily used qualitatively for verifying patient setup.
Table 1.2 summarises the clinical applications of EPIDs. Of increasing interest is
portal dosimetry – quantitative use of portal images for 2D dose verification. The
demand is largely driven by the clinical need for efficient IMRT verification. Two
approaches to using portal dosimetry for treatment verification are:
- forward portal dose prediction, where the treatment-time image is com-
pared against the predicted image; and
- patient dose reconstruction, where the treatment-time image is used to
derive the dose actually received by the patient.
So far, efforts in portal dose prediction have been generally based on:
∗e-Science refers to the large scale science carried out through distributed global collaborationsenabled by the Internet. Such collaborative scientific enterprises typically require access to verylarge data collections, very large scale computing resources and high performance visualisation.
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CHAPTER 1. INTRODUCTION 13
Table 1.2: Clinical applications of EPIDs.
Application ReferencesPatient setup verifica-tion
Lam et al. [1993], Elgayed et al. [1993], Hunt et al. [1995],Bel et al. [1995], Luchka and Shalev [1996], Pouliot andLirette [1996], Millar et al. [1997], Yan et al. [1998],Girouard et al. [1998], Boxwala et al. [1999], Samson et al.[1999], Pisani et al. [2000], de Boer et al. [2001], Hatherlyet al. [2001], Phillips et al. [2002], Vetterli et al. [2004]
MLC trajectory verifi-cation
Keller et al. [1998], Partridge et al. [2000], James et al.[2000], Chen et al. [2002], Ploeger et al. [2002], Popescuet al. [2002], Samant et al. [2002], Vieira et al. [2002],Fielding et al. [2002], Obcemea et al. [2003], Sonke et al.[2004], Chang et al. [2004]
Linac QA Kirby and Williams [1995], Luchka et al. [1996], Hierholzet al. [1999]
Compensator designand verification
Roback and Gerbi [1995], Evans et al. [1998], Menon andSloboda [2003]
Organ motion studies Vigneault et al. [1997], Kroonwijk et al. [1998], Kuboet al. [1999], Vantienhoven et al. [1991], Kaatee et al.[2002], Ford et al. [2002], van Asselen et al. [2003],Berbeco et al. [2003]
2D dose verification Yin et al. [1994], Zhu et al. [1995], Essers et al. [1996],McNutt et al. [1996, 1997], Boellaard [1998], Keller et al.[1998], Curtin-Savard and Podgorsak [1999], Pasma et al.[1999], El-Mohri et al. [1999], Chang et al. [2001], vanEsch et al. [2001], McCurdy et al. [2001], Spezi and Lewis[2002], Grein et al. [2002], Chang et al. [2002], Islam et al.[2003], Greer and Popescu [2003], Warkentin et al. [2003],van Esch et al. [2004]
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CHAPTER 1. INTRODUCTION 14
- convolution/superposition algorithms, which ignore spectral differences and beam
hardening, and can be inaccurate particularly when scatter conditions differ
from that of the one-time scatter kernel generation. These algorithms have
been adopted in all dosimetric work cited in Table 1.2 except Keller et al.
[1998], Spezi and Lewis [2002] and Siebers et al. [2004].
- image-to-dose calibration which assumes the EPID to be dosimetrically water-
equivalent. This assumption is inherent of all convolution/superposition work
cited in Table 1.2 except McCurdy et al. [2001] and Warkentin et al. [2003].
These features impose some constraints, such as:
- the EPID must be placed at least 80 cm away from the patient exit plane
[Boellaard 1998], which is clinically impractical; and
- no attenuating objects such as a patient or a phantom could be included in the
calculation [van Esch et al. 2004], thereby ruling out on-treatment verification.
This PhD project (April 2002 to March 2005) provides a MC solution for radiotherapy
verification of external photon beams, developing work initiated within the same
institution [Spezi and Lewis 2002]. In addition to overcoming the limitations of
convolution/superposition methods, the work developed herein allows portal dose
prediction for oblique beams, which has not been previously reported.
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CHAPTER 1. INTRODUCTION 15
CHAPTER 5
A MONTE CARLO SOLUTIONTREATMENT VERIFICATION:
CHAPTER 3MONTE CARLORADIATION TRANSPORT
CHAPTER 2PORTAL IMAGING
CHAPTER 8HIGH THROUGHPUTCOMPUTING
CHAPTER 7PRACTICAL ASPECTS OFIMAGE ACQUISITION
CHAPTER 6OPTIMISATION OFMONTE CARLOSIMULATIONS
CHAPTER 4SIMULATION OFLINAC SOURCES
BACKGROUND
KNOWLEDGE
THEORY & OPTIMISATION,
IDEAS
SOLUTIONS &
AS INPUT FOR
SUBSEQUENT
SIMULATIONS
TOWARDS
CLINICALLY
ACCEPTABLE
RUN TIMES
Figure 1.6: Thesis structure.
1.6 Thesis Structure
Chapter 5 is the core of the thesis where its main objective is accomplished. It reports
the development of a treatment verification solution which combines the accuracy of
MC simulations with the technology of EPIDs. As outlined in Figure 1.6, the other
chapters support Chapter 5. Chapters 2 and 3 lay out the theory and background
knowledge fundamental to the scope of the thesis. Chapter 4 details the MC simu-
lation of a medical linear accelerator; simulation output from here was subsequently
used as radiation source for simulations in Chapter 5. Chapter 6 and 7 further en-
hance the treatment verification solution by introducing optimisation, new ideas and
solutions to problems. Chapter 8 describes how the long run times of MC simulations
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CHAPTER 1. INTRODUCTION 16
may be overcome with several levels of High Throughput Computing∗ (HTC), includ-
ing the Grid; this prepares for clinical implementation of the treatment verification
solution. Chapter 9 concludes the thesis.
As will be summarised in Table 9.1 and listed in Appendix A, some content of this
thesis has already been published in journals and conference proceedings during the
project. For all the work reported, the author has been the lead author. Co-authors
and collaborators contributed in the form of supervision or technical assistance. It is
in this context that “we” is sometimes used in the chapters that follow.
∗High Throughput Computing is an environment that can deliver large amounts of processingcapacity over long periods of time.
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Chapter 2
ELECTRONIC PORTAL
IMAGING
Electronic portal imaging devices (EPIDs) have been introduced in Section 1.2. This
chapter begins by introducing the key parameters quantifying imager performance,
followed by a discussion on the EPID technologies investigated in this thesis: the
scanning liquid ion chamber (SLIC) and the amorphous silicon (a-Si) EPIDs.
2.1 Imager Performance
Fundamentals of medical radiography are covered in several textbooks (e.g. Barrett
and Swindell [1981], Webb [1988], Hasegawa [1991]). A portal image is formed by
a scatter fluence component added to a primary fluence component; the combined
fluence is then modulated by the detector response. In the following section, quantities
giving an objective measure of image quality will be described in three levels:
1. basic quantities: contrast, spatial resolution and noise;
17
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CHAPTER 2. ELECTRONIC PORTAL IMAGING 18
2. integrating quantities: modulation transfer function (MTF) and signal-to-noise
ratio (SNR);
3. unifying quantity: detective quantum efficiency (DQE).
Contrast describes how much an object stands out from its surroundings. It can
be defined by taking into account of the image formation process (Figure 2.1) and is
described using
contrast =φp1 − φp2
φp1
(2.1)
where φp1 and φp2 are as defined in Figure 2.1. From Equation (2.1), it can be seen that
the greater the difference in attenuation of the object from that of the background, the
better the contrast. Due to the strong Z-dependence of photoelectric cross sections,
bony structures are differentiated better than soft tissues.
Figure 2.1: Image formation in x-ray transmission radiography. φp1 and φp2 are photonfluences reaching the image receptor attenuated and unattenuated by the anatomic structurerespectively; φs is the scatter fluence reaching the detector. Reproduced from Herman et al.[2001].
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CHAPTER 2. ELECTRONIC PORTAL IMAGING 19
Spatial resolution describes how well edges can be detected. This is the minimum
distance at which two objects may be resolved. It depends on the source size, pixel
size and image magnification.
Noise in a radiographic image is the uncertainty in signal arising from two main
sources:
1. statistical fluctuations in the number of photons detected per unit area (quan-
tum noise);
2. fluctuations due to the properties of the imaging receptor and the display sys-
tem.
INC
RE
AS
ING
CO
NT
RA
ST
DECREASING NOISEDECREASING NOISE
INC
RE
AS
ING
RE
SO
LU
TIO
N
Figure 2.2: Interplay between contrast, resolution and noise on the detectability of a whitedisc against a black background. Images have been extracted from www.ge.com.
Figure 2.2 shows the interplay between contrast, spatial resolution and noise on
the detectability of a white disc against a black background. Detectability is low
when: 1) the noise is high even if the contrast or resolution is excellent; or 2) the
noise is minimal but the contrast or resolution is poor. By itself, none of the three
quantities is adequate in characterising imager performance.
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CHAPTER 2. ELECTRONIC PORTAL IMAGING 20
To gauge the interplaying effects between contrast and resolution, the MTF was
defined. It is calculated from the Fourier transform of the point spread function. The
MTF measures the sharpness, or blur, by characterising how well the system passes
different spatial frequencies.
To gauge the interplaying effects between contrast and noise, the SNR was defined:
SNR =φp2 − φp1√
12(φp2 + φp1 + 2φs)
(2.2)
φp1, φp2 and φs are as given in Figure 2.1. The SNR varies through various stages of
image production as more noise is introduced.
The DQE combines the effects of all three basic quantities: contrast, resolution and
noise. It tells how efficient the imaging system is at transferring the input information
to the output image.
DQE =
(SNRoutput
SNRinput
)2
(2.3)
It should be emphasised that SNRoutput should be measured at a point in the detect-
ing system following which no further degradation in SNR is observed [Barrett and
Swindell 1981]. The single parameter DQE is representative of image quality and
object detectability. Maximising the DQE is therefore the ultimate goal in imager
design.
2.2 Megavoltage Imaging
A transmission imaging system consists of a radiation source, the object being im-
aged and a detector (Figure 2.3). EPIDs, like diagnostic X-ray units, are transmission
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CHAPTER 2. ELECTRONIC PORTAL IMAGING 21
OBJECT
SOURCE
DETECTOR
Figure 2.3: A transmission imaging system. X rays transmitted through the object beingimaged are detected by the detector.
imaging systems. Electronic portal images (EPIs) are projection maps of photon at-
tenuation (and scatter), similar to X-ray images. Megavoltage (MV) imaging with
EPIDs, however, differs from kilovoltage (kV) imaging with diagnostic X-ray ma-
chines, as summarised in Table 2.1. Megavoltage images are generally considered
poorer in image quality than the kilovoltage equivalent, due to the decrease in con-
trast, increase in scatter, and the larger size of the radiotherapy source.
Figure 2.4 illustrates visually the difference between kV and MV imaging. On the
kV image, bony structures are particularly clear due to high photoelectric absorption
in bone. On the MV image, bones are invisible because the dominant process is
Compton scattering, which is almost independent of Z. Instead, image contrast is
provided by differences in density. Poor discrimination of bony structures at the
MV range is explained in Figure 2.5 which plots the bone-to-water and air-to-water
contrasts.
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CHAPTER 2. ELECTRONIC PORTAL IMAGING 22
Table 2.1: Kilovoltage versus megavoltage imaging.
Kilovoltage MegavoltageImage function Morphological diagnosis. Radiotherapy record, verification
and rectification.Design Optimised for excellent im-
age quality.Constrained to an environmentoptimised for treatment.
Dominantinteraction
Photoelectric absorption,which depends on atomicnumber of object to thepower of 3 to 5.
Compton scatter, which dependson electron density of object.Hence, poorer bone-to-air con-trast.
Scatter-to-primary ratio
Lower. Higher [Jaffray et al. 1994,Swindell and Evans 1996, Spiesand Bortfeld 2001, Ozard andGrein 2001]. Scatter adds noiseto images.
Main cause ofimage blur
K-shell fluorescence andtransport of optical photonswithin the scintillator.
Scattered photons and electrons.
Source size Less than 0.1 mm. 0.5 mm to 3.4 mm [Jaffray et al.1993]. Hence, decreased resolu-tion and sharpness.
Penetration ofsource
Lower. Higher. Hence, decreased detec-tion efficiency.
2.3 The SLIC and the a-Si Technologies
Several EPID technologies have evolved to improve megavoltage imaging during ra-
diotherapy. The SLIC EPID was originally developed at the Netherlands Cancer
Institute [van Herk 1991] before being commercialised. A non-optical system, it is
compact and glare-free, unlike camera-based systems which impose bulky construc-
tion, image spatial distortion and non-uniformity commonly known as “glare” [Heij-
men et al. 1995, Partridge et al. 1999]. The frame-rate of the SLIC EPID is, however,
less than 1 fps (frame per second), which is too slow for imaging a dynamic multileaf
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CHAPTER 2. ELECTRONIC PORTAL IMAGING 23
Figure 2.4: Kilovoltage versus megavoltage imaging: chest x rays of the same patient takenon 80 kV (left) and 2 MV (right) x ray machines. Reproduced from Johns and Cunningham[1983].
collimator (DMLC∗) beam delivery.
Compared to the SLIC EPID, the a-Si EPID has a higher frame rate (over 3 fps
depending on the acquisition mode), a larger detection area (40.0 cm × 30.0 cm)
and a higher resolution (0.78 mm). It couples the phosphor scintillator screen with a
large-area active matrix readout. The unique technology underlying active matrix flat
panel imagers (AMFPIs) is large-area integrated circuits called active-matrix arrays
[Antonuk et al. 1997]. The technology allows deposition of semiconductors (e.g. a-
Si) across large-area substrates such that physical and electrical properties of the
structures can be adapted for a variety of applications.
Stages of radiation detection in the SLIC and the a-Si EPIDs will now be described.
Figure 2.6 depicts schematically a typical portal imaging cassette. The converter
converts the incident radiation into a form detectable by the detector. Together these
∗DMLC leaves move while the beam is on. Beamlets depicted in Figure 1.2 are delivered contin-uously without switching off the beam (for rearrangement of leaves).
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CHAPTER 2. ELECTRONIC PORTAL IMAGING 24
Figure 2.5: Subject contrast for a 1 cm bony structure and a 1 cm air cavity embeddedin water. Reproduced from Herman et al. [2001].
two layers form “the heart” of the imager:
• the converter may be a metal plate or a combination of a metal plate and a
scintillating screen. It stops incident photons so that they may be detected.
- For the SLIC EPID, the converter is a 1 mm-thick plastoferrite∗ plate
which converts photons into high-energy electrons and screens out low-
energy scattered radiation.
- For the a-Si EPID, the converter is a combination of a copper plate and a
phosphor screen: a 1 mm-thick copper plate converts photons into high-
energy electrons, at the same time blocking off low-energy scattered radi-
ation; a phosphor scintillating screen† converts electrons into light. The
presence of the phosphor improves sensitivity and efficiency [Munro and
Bouius 1998].
∗The plastoferrite is a compound containing iron and strontium.†This is a Gd2O2S:Tb (gadolinium oxysulphide terbium activated) screen.
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CHAPTER 2. ELECTRONIC PORTAL IMAGING 25
BACK COVER
DETECTOR
CONVERTER
FRONT COVER
MEGAVOLTAGESOURCE *
SO
UR
CE
−SU
RF
AC
E D
IST
AN
CE
(S
SD
)
SO
UR
CE
−DE
TE
CT
OR
DIS
TA
NC
E (
SD
D)
PHANTOM−EPID SEPARATION
Figure 2.6: Schematic of a generic portal imaging cassette, shown with a megavoltagesource irradiating a phantom. Dimensions are not drawn to scale.
• the detector is analogous to the piece of film used in traditional portal imaging.
- For the SLIC EPID, the detector is a layer of iso-octane∗ which serves as
the ionising medium for incident electrons. At each pixel, an electrometer
converts ionisation into electrical signals.
- For the a-Si EPID, the detector is a glass substrate containing an array of
hydrogenated amorphous silicon (a-Si:H) photodiodes and thin film tran-
∗The iso-octane is an organic liquid, 2,2,4 trimethylpentane.
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CHAPTER 2. ELECTRONIC PORTAL IMAGING 26
sistor (TFT) switches. At each pixel, the photodiode-TFT pair converts
light into electrical signals.
Unlike films, where signals are detected and stored on the film itself, detectors
in EPIDs detect but do not store – data is stored digitally.
The converter and the detector are sandwiched between the front and the back pro-
tective housings. Interleaved between these layers are multiple internal protective
layers e.g. foam-like materials, which are not shown in the figure.
Analogous to films, which detect radiation effects in the form of chemical tran-
sitions, the SLIC and the a-Si EPIDs detect such effects in the form of ionisation
in liquids and electrical conductivity in solids respectively. Monte Carlo studies of
radiation transport in the SLIC and the a-Si EPIDs will be presented in Chapter 6.
Practical issues concerning the use of both EPIDs will be discussed in Chapter 7.
Some key points here will suffice:
- the liquid thickness in the SLIC EPID varies with cassette orientation, causing
the detector response to change with gantry angle;
- unclean discharge and charge trapping in the a-Si EPID cause “ghosting” in
subsequent image frames; and
- limitations of acquisition systems e.g. synchronisation with linac pulses and
integration of multiple frames complicate radiotherapy verification somewhat.
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Chapter 3
MONTE CARLO RADIATION
TRANSPORT
Most “experiments” described in this thesis involve computer simulations of stochas-
tic processes in radiation physics – Monte Carlo (MC) radiation transport. Events
simulated include transport, interaction and energy deposition of radiation particles
in computer representations of the linac, the patient, the electronic portal imaging
device (EPID) and the surrounding air. Photons, electrons and positrons were simu-
lated. Since the presence of neutrons is negligible in the energy range of interest (6
MV), they were not simulated. Referring to Figure 1.1, simulation of effects such as
chemical changes and biological damage are beyond the scope of this thesis.
3.1 Analog and Non-analog Simulation
The MC technique uses probability distributions of various interactions to simulate
the transport, interaction and energy deposition of individual particles in matter.
Figure 3.1 steps through the logic behind a typical analog transport for a simplified
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CHAPTER 3. MONTE CARLO RADIATION TRANSPORT 28
Y
Y
N
N
READ POSITION, DIRECTION & ENERGY OF PARTICLE
ENERGY CUTOFF?BELOW
DISCARD PARTICLE
DISCARD PARTICLE
SIMULATION UNIVERSE?OUTSIDE
SAMPLE DIRECTION & ENERGY OF RESULTANT PARTICLES
INTERACTION OCCURS
TRANSPORT PARTICLE TO INTERACTION SITE
Figure 3.1: Logic in a typical analog transport.
case of a homogeneous single-element geometry. This logic is repeated for all primary
and secondary particles. An analog transport samples every single event explicitly.
Photons are usually simulated this way.
Full step-by-step simulation, however, becomes unrealistic for electrons. There
are simply too many interactions. For example, electrons typically undergo 7000
elastic scatterings in slowing down from 500 to 250 keV in gold [Berger and Wang
1988]. To circumvent this difficulty, the cumulative effect of multiple interactions is
approximated into a single step. The artificial step length is often chosen to be many
mean free paths. This is known as the condensed history technique.
An implementation of condensed history for charged particles is shown in Fig-
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CHAPTER 3. MONTE CARLO RADIATION TRANSPORT 29
ELASTIC COLLISIONS
SUBTHRESHOLD EVENTS
CHARGED PARTICLE INTERACTIONS
CONTINUOUS ENERGY
LOSS MODEL
DISCRETE EVENTS
SCATTER
MOLLER / BHABHA
INELASTIC COLLISIONS
THEORY
MULTIPLE−SCATTER
PRODUCTION
BREMSSTRAHLUNG
Figure 3.2: An implementation of condensed history for charged particle transport.
ure 3.2∗. Elastic collisions are treated using multiple-scatter theories [Kawrakow
2000a, Moliere 1948, Goudsmit and Saunderson 1940]. Inelastic collisions are divided
into two groups according to the threshold energy: subthreshold inelastic collisions
are treated using continuous energy loss models (for energy loss) and multiple-scatter
theories (for angular deflection); above-threshold inelastic events are simulated explic-
itly event-by-event. The condensed history technique fits into a modified transport
logic (Figure 3.3) different from that shown in Figure 3.1. Non-analog simulations
such as these, when properly implemented and applied, should not cause any bias in
simulation outcome.
∗This is the implementation for EGS; implementation in MCNP differs.
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CHAPTER 3. MONTE CARLO RADIATION TRANSPORT 30
Y
N
ENERGY CUTOFF?BELOW
DISCARD PARTICLE
SAMPLE DIRECTION & ENERGY OF RESULTANT PARTICLES
DISCRETE INTERACTION OCCURS
MULTIPLE SCATTER STEP
READ POSITION, DIRECTION & ENERGY OF PARTICLE
N
Y
N
DISCARD PARTICLE
N
Y
SIMULATION UNIVERSE?OUTSIDE
ENERGY CUTOFF?BELOW Y DISCARD PARTICLE
CALCULATE DISTANCE TO DISCRETE INTERACTION
INTERACTION POINT?REACHED DISCRETE
Figure 3.3: Logic in electron transport. Dashed box outlines the difference from Figure 3.1.
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CHAPTER 3. MONTE CARLO RADIATION TRANSPORT 31
3.2 Why Monte Carlo?
As will be demonstrated in later chapters, MC simulation of radiation transport is
tremendously powerful:
- it is more accurate than deterministic or analytical calculations particularly
under conditions of electronic disequilibrium, mainly due to the complexity of
electron transport;
- it allows tally∗ placement in areas not accessible by physical measurements, e.g.
a point inside a patient’s spinal cord;
- it provides information not extractable from physical measurements, e.g. the
fraction of particles originating from Compton scatter within a particular region
of interest;
- it provides a “virtual” experimental platform not available otherwise, e.g. trial-
and-error iterations of various beam configurations on a “virtual patient”;
- it facilitates detailed understanding of radiation physics e.g. stages of radiation
detection in a detector.
3.3 Choice of Codes
MC code systems are complex. They require substantial development and bench-
marking efforts. Large user-bases contribute towards more error-reporting and hence
∗The tally is a quantitative outcome requested by the user from the MC simulation, e.g. dose ina specific region.
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CHAPTER 3. MONTE CARLO RADIATION TRANSPORT 32
improve code integrity. Established MC code systems include EGS (Electron Gamma
Shower) developed by the Stanford Linear Accelerator Center and the National Re-
search Council of Canada [Nelson et al. 1985, Kawrakow 2000a], and MCNP (Monte
Carlo N-Particle) by Los Alamos National Laboratory [Briesmeister 1986, 1993]. Each
evolves incrementally through code versions, for improved physics and sometimes for
wider compatibility (e.g. executable on desktop Windows machines or capable of
built-in parallel processing).
MC code systems differ in certain aspects and features such as:
- sampling algorithms, e.g. the new EGS version, EGSnrc [Kawrakow 2000a], has
been shown to achieve unprecedented accuracy in electron transport [Kawrakow
2000b];
- implementation of condensed history, e.g. EGS simulates bremsstrahlung pro-
cesses above a certain energy threshold but MCNP does not;
- particle types simulated, e.g. MCNP simulates neutrons but EGS does not;
- variance reduction techniques∗ [Briesmeister 1986, Kawrakow et al. 2004] avail-
able, e.g. MCNP offers a wider range of techniques;
- statistical analysis tools available, e.g. MCNP has its ten statistical tests whereas
EGS only computes the standard error; and
∗Variance reduction techniques increase simulation efficiency by modifying the conventional ran-dom walk sampling, e.g. by preferentially sampling particles that would be more likely to eventuallycontribute to the tally.
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CHAPTER 3. MONTE CARLO RADIATION TRANSPORT 33
- user-base for specific applications, e.g. EGSnrc has the wider radiotherapy
user-base.
3.4 EGSnrc, BEAMnrc and DOSXYZnrc
For accuracy in electron transport and applicability to radiotherapy problems, the
EGSnrc code system was chosen for the work in this thesis. EGSnrc takes into
account the following photon, electron and atomic processes:
- pair production (triplet production is not simulated explicitly but is taken into
account using a combined pair-and-triplet cross section compiled by Storm and
Israel [1970])∗;
- Compton scatter, with options for Klein-Nishina (which assumes electrons to
be free) or bound Compton [Johns and Cunningham 1983];
- photoelectric effect;
- Rayleigh scattering, if requested;
- Bremsstrahlung production;
- Møller and Bhabha scattering;
- positron annihilation in flight and at rest;
∗In a pair production, the photon interacts with the Coulomb field of the nucleus and isabsorbed; an electron-positron pair is created. In a triplet production, the photon interacts with thefield of an atomic electron which receives sufficient energy to be set free.
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CHAPTER 3. MONTE CARLO RADIATION TRANSPORT 34
- multiple scattering of charged particles by Coulomb scattering from nuclei
[Kawrakow 2000a];
- collision energy loss determined by the restricted Bethe-Bloch stopping powers
with Sternheimer treatment of density effects;
- relaxation of excited atoms following vacancies (due to photoelectric or Comp-
ton events), if requested, producing K, L and M shell fluorescent photons, Auger
and Coster-Kronig electrons.
EGSnrc, and its radiotherapy-related derivatives BEAMnrc [Rogers et al. 2001]
and DOSXYZnrc [Walters and Rogers 2002] were used in various parts of this thesis:
- EGSnrc requires extensive programming but offers greatest flexibility. For in-
stance, particle-labelling (to track information through generations of secondary
particles) and tallies may be placed at any point in the logic shown in Figure 3.1
and Figure 3.3. EGSnrc was used in detailed investigations such as detector
studies (Chapter 6).
- BEAMnrc is a specialised code for modelling of linear accelerators (linacs). It
contains a library of component modules (CMs) such as the flattening filter∗ and
the collimators. The user assembles the geometry by selecting the appropriate
components and specifying the dimensions. BEAMnrc was used in simulation
of radiotherapy sources (Chapter 4).
∗In the megavoltage range, the bremsstrahlung photon beam is peaked in the forward direction.A flattening filter is inserted in the beam to make the intensity uniform across the beam.
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CHAPTER 3. MONTE CARLO RADIATION TRANSPORT 35
- DOSXYZnrc is a specialised code for tallying dose deposition in a rectilinear
voxel geometry. When detailed representation of the inhomogeneous patient
body is required, it is capable of importing voxel-by-voxel material and density
data from CT scans. DOSXYZnrc was used for dose calculation in phantoms
and detectors (Chapter 5). TWIZ&GLU, a pre-processor designed and imple-
mented by the author, extended the usability of DOSXYZnrc for portal dose
computation of oblique beams [Chin et al. 2003].
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Chapter 4
SIMULATION OF LINAC
SOURCES
Accurate Monte Carlo (MC) simulation of clinical beams is essential for providing
a realistic representation of radiotherapy sources for dose calculations. At Velindre
Cancer Centre, production of photon beams from the medical linear accelerator (linac)
has previously been simulated using an earlier BEAM version, BEAM00 [Rogers et al.
2000]. This chapter reports simulation of linac photon beams using the recent version,
BEAMnrc [Rogers et al. 2001], which incorporates improved physics and statistical
estimation.
The range of field sizes simulated was broader than that previously available. Out-
put from this chapter equips our data library with computer representations of linac
photon beams, which can be readily deployed in further simulations (e.g. simulations
in the next chapter) so that the same linac need not be simulated repeatedly.
This chapter also covers investigations on transport options, variance reduction
techniques∗ and statistical uncertainties – all of which are of great scientific interest.
∗Variance reduction techniques have been introduced in Section 3.3.
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CHAPTER 4. SIMULATION OF LINAC SOURCES 37
4.1 Introduction
As introduced in Section 3.4, BEAM is a specialised MC code for linac modelling.
It is built on EGS, which has evolved incrementally through code versions. EGSnrc
is the version used for this thesis except in Section 4.2.1 where, for comparison pur-
poses, an earlier version was also used. EGSnrc is the first MC code to pass the
most stringent benchmark tests, by successfully simulating ion chamber response and
backscatter artefact-free [Kawrakow 2000b]. Since the new features of EGSnrc have
been incorporated in BEAMnrc but not BEAM00, BEAMnrc is understood to be
more accurate in radiation transport physics. Additionally, as will be explained in
Section 4.2.5, an improved statistical estimation in BEAMnrc accounts for the corre-
lation between secondary particles originating from the same source particle [Walters
et al. 2002]. We have therefore simulated our linac photon beams using BEAMnrc
and recommissioned our phase space library.
Whereas clinical beams are sometimes MC-simulated “one-off” for generating ker-
nel libraries required in convolution/superposition methods, there are growing inter-
ests in using the output for subsequent case-by-case, patient-dependent MC simu-
lations. MC simulation of clinical beams has been reported by various groups and
has been extensively reviewed (see Verhaegen and Seuntjens [2003] and references
therein). Most reports, however, deal with a limited range of field sizes, or lack rigor-
ous analysis of deviation from measured data. To our knowledge, none have reported
effects of the improved EGSnrc transport physics on linac beam simulation.
In this work, we explored different transport configurations in the simulation of
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CHAPTER 4. SIMULATION OF LINAC SOURCES 38
a Varian linac. A fine-tuned model of the 6 MV photon beam was found to produce
good agreement with measured beam data for 6 tested field sizes ranging from 2 cm
× 2 cm to 25 cm × 25 cm.
Section 4.3.5 reports some interesting and unexpected effects on statistical uncer-
tainty when simulating an increasing number of particles. Step-by-step investigations
to trace the cause will be presented, along with a new method for validating that a
phase space file∗ is an adequately representative sample of a beam.
4.2 Materials & Methods
BEAM00, BEAMnrc and DOSXYZnrc were used for simulations in this chapter:
- a Varian Clinac 2100CD linac was simulated using BEAM00 (Section 4.2.1) and
BEAMnrc (Section 4.2.1, Section 4.2.2, Section 4.2.3, Section 4.2.4);
- dose deposition in a water phantom was simulated using DOSXYZnrc (Sec-
tion 4.2.3, Section 4.2.4 and Section 4.2.5).
Table 4.1 gives a general description of the above simulations according to the frame-
work, “How Monte Carlo simulations work” given in Figure 1.4.
∗To avoid repeated simulations of the same linac, a phase space file is often stored to be usedas the radiation source in subsequent dosimetric simulations. It contains data for many particles:one record for each particle crossing a user-specified plane (Figure 4.1). Each record contains theposition, direction, energy and statistical weight for one particle.
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CHAPTER 4. SIMULATION OF LINAC SOURCES 39
Table 4.1: Description of simulations performed in this chapter.BEAM00/BEAMnrc DOSXYZnrc
Geometry A computer representation of thelinac was constructed by assemblingvarious linac components e.g. thetarget, the flattening filtera and thejaws according to compositions anddimensions provided by the manufac-turerb (Figure 4.1). The same linacmodel was used throughout the chap-ter except in Section 4.2.4, where theopening of the jaws was varied to pro-vide the desired range of field sizes.
A computer representationof a water phantom was con-structed as a 3D lattice ofvoxels (Figure 4.2).
Source A parallel beam of monoenergeticelectrons impinging on the linac tar-get, a tungsten-copper composite(Figure 4.1). In Section 4.2.3, theenergy and the radius of this elec-tron source were varied to obtain thebest agreement between simulationresults and measured beam data.
A phase space file producedfrom BEAMnrc simulations.
Transport Transports using BEAM00 andBEAMnrc were compared in Sec-tion 4.2.1. For BEAMnrc, anoptimised set of transport optionswas determined in Section 4.2.2and was used in all subsequentsimulations in the chapter.
DOSXYZnrc default trans-port options were used.
Output A phase space file. Dose deposition in eachvoxel in the 3D lattice.
aThe flattening filter has been introduced in Section 3.4.bExact details cannot be provided here due to confidential agreements with the manufacturer.
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CHAPTER 4. SIMULATION OF LINAC SOURCES 40
Y JAWS
X JAWS
QUADRANT 1
QUADRANT 4
QUADRANT 2QUADRANT 3
R
G
L
T
ELECTRONSINCIDENT ONTARGET
PHASE SPACE PLANE
Figure 4.1: BEAMnrc simulation of a linac, where a pencil beam of electrons impinges onthe linac target. The phase space plane is defined downstream from the linac. Locationof X and Y jaw pairs at different levels causes asymmetry in the GT (“Gun-Target”, alsoknown as inplane) and LR (“Left-Right”, also known as crossplane) directions on the phasespace plane. Particle tracks are also shown.
4.2.1 Migration from BEAM00 to BEAMnrc
To see whether BEAM00 and BEAMnrc produce the same output when the same
linac model (geometry) is simulated, simulations were run using the two codes. The
phase space files produced were analysed for photon fluence.
4.2.2 Selection of Transport Options
BEAMnrc was used in all sections that follow. For selecting an optimised set of
transport options, 3 transport configurations were considered:
- configuration A: detailed transport, henceforth referred to as “first-class” trans-
port, understood to produce unprecedented accuracy, made possible by the re-
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CHAPTER 4. SIMULATION OF LINAC SOURCES 41
lease of EGSnrc. No variance reduction techniques were used. This served as
the reference against which other configurations were compared.
- configuration B: transport using BEAMnrc default settings. No variance reduc-
tion techniques were used. Investigation of this configuration was to indicate the
necessity for caution when adopting the default settings “off-the-shelf”. These
default settings would be in effect whenever the settings were not explicitly
specified.
- configuration C: transport with variance reduction. Bremsstrahlung splitting∗
and Russian roulette† were used to increase simulation efficiency. In this con-
text, efficiency measures the number of phase space particles produced within
a given simulation time, rather than the conventional history-per-time gauge.
Settings of transport options are given in Table 4.2. Details on the transport
options and variance reduction techniques used are given in the literature [Kawrakow
and Rogers 2002, Kawrakow 2000a]. In all three configurations, a 6.0 MeV electron
source of radius 1.0 mm was simulated. Jaw settings were modelled for a 5 cm × 5
cm field‡.
Output from all three configurations was tested individually for:
∗Bremsstrahlung splitting is a variance reduction technique where a bremsstrahlung event pro-duces X photons, each with 1/X statistical weight, instead of a single photon with unity statisticalweight. This is to improve the statistics of bremsstrahlung photons.
†Russian roulette is a variance reduction technique which imposes a survival threshold on sec-ondary charged particles from photons generated by bremsstrahlung splitting. Depending on therandom number generated for each charged particle and the survival threshold, the particle eithersurvives the roulette or is eliminated.
‡All field sizes in this thesis are defined at the level of the isocentre, which, for the installationsused in this work, is 100.0 cm away from the source and 124.5 cm above the floor. The isocentre isthe point where the central axis of all beams intersect when the gantry is rotated.
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CHAPTER 4. SIMULATION OF LINAC SOURCES 42
Table 4.2: Configurations A, B and C for BEAMnrc simulation of linac sources.A B C
Boundary crossing algorithma EXACT PRESTA-I EXACTElectron-step algorithm PRESTA-II PRESTA-II PRESTA-II
Spin effects On On OnPhotoelectron angular samplingb On Off On
Bound Compton scattering On Off OnAtomic relaxations On Off On
Electron cutoff (MeV including rest-mass) 0.521 0.521 0.700Uniform bremsstrahlung splitting 0 0 500
Russian roulette Off Off On
a’EXACT’ switches into single elastic scattering mode near boundaries.bSauter’s formula if ’On’ [Sauter 1931].
- photon energy fluence and energy spectrum on the phase space plane; and
- dose deposition in a water phantom simulated using DOSXYZnrc, where the
phase space output from the BEAMnrc simulation served as the radiation
source.
4.2.3 Fine-tuning the Linac Model
The initial model of 6.0 MeV electron pencil beam with a 1.0 mm source radius was
further fine-tuned for better agreement with dose characteristics in a water phantom.
In the fine-tuning process, the incident electron energy was varied from 5.85 MeV
to 6.10 MeV; the source radius was varied from 0.5 mm to 2.5 mm. A 5 cm × 5
cm field was chosen for the fine-tuning process since smaller fields were found to
be more sensitive to variations in incident electron energy and source dimension.
Moreover, smaller field sizes are of greater interest since they are commonly used for
high-precision radiotherapy.
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CHAPTER 4. SIMULATION OF LINAC SOURCES 43
Dose deposition in a water phantom was simulated using DOSXYZnrc, where
phase space output from the BEAMnrc simulation served as the radiation source.
The in-phantom depth doses and radiation profiles were compared against measured
beam data obtained during linac commissioning∗. The source model producing the
best agreement with measured beam data was chosen to be the fine-tuned model.
4.2.4 Modelling Varying Field Sizes
By changing the jaw positions in the linac model, square fields of varying dimensions
were simulated: 2 cm, 5 cm, 10 cm, 15 cm, 20 cm and 25 cm.† For each field size, dose
deposition in a 50 cm × 50 cm × 50 cm water tank, simulated using DOSXYZnrc,
was compared against measured beam data obtained during linac commissioning.
For dose deposition in a water tank, 3.0 cm × 0.2 cm voxels of varying thicknesses
were defined along the central axis (Figure 4.2). The thickness was 0.2 cm for the
first 5.0 cm depth, and 1.0 cm for further depths. This was used for all incident field
sizes except field size 2 cm × 2 cm, where 1.0 cm × 0.2 cm voxels were used instead
of 3.0 cm × 0.2 cm.
Simulation output for dose deposition is in units of Gray per incident radiation
history, usually of the order of 10−17. Measured beam data is obtained in percentage
terms, relative to the maximum reading (for depth doses), or to the central axis
reading (for transverse radiation profiles). Normalisation is therefore required before
∗An ion chamber was used for measuring depth doses; a diode was used for measuring transverseprofiles.
†For portal dosimetry (the topic of this thesis), 25 cm × 25 cm is the maximum field of interest.It is the maximum allowable field when the EPID is positioned at 130 cm from the source; themaximum allowable field is even smaller when the EPID is further away from the source.
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CHAPTER 4. SIMULATION OF LINAC SOURCES 44
0.2 cm
3.0 cm
1.0 cm
0.2 cm
0.2 cm
3.0 cm
50 cm
50 cm
50 cm
5 cm
23.5 cm
23.5 cm
Figure 4.2: Voxel geometry used for tallying dose deposition in a 50 cm × 50 cm × 50cm water tank: 3.0 cm × 0.2 cm voxels of varying thicknesses were defined as shown. Thethickness was 0.2 cm for the first 5.0 cm depth, and 1.0 cm for further depths.
simulation results may be compared against measured data. Figure 4.3 explains each
step in the normalisation procedure. Normalised in this way, radiation profiles would
have depth dose data included implicitly. Explicit plotting of depth dose curves for
comparing the two datasets would therefore not be necessary.
4.2.5 Use of Phase Space Particles
In using phase space files to provide source particles for subsequent simulations e.g.
portal image prediction (Chapter 5), there are two sources of uncertainty in the
subsequent simulations:
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CHAPTER 4. SIMULATION OF LINAC SOURCES 45
NORMALISETO D9
NORMALISETO D9
NORMALISETO
NORMALISETO
depth dose profile profile
1.5D
9D
D9 E9
E9
D15D21D27
READY FOR COMPARISON
15D
D21D27
D1.5
RESPECTIVELY
D 1.5, D 9, D15, D21
and D27
NORMALISE EACH TO
MEASUREMENTS SIMULATIONS
c) e)a)
d)b) f)
Figure 4.3: Schematic diagram of the normalisation procedure for comparing measuredbeam data with MC simulation results. From a to b: normalising the measured depth dosecurve to the relative dose value D9, which is the vertical-axis value at depth 9.0 cm. From b:deriving D1.5, D15, D21 and D27, which are the relative dose values corresponding to depths(horizontal axis) 1.5 cm, 15 cm, 21 cm and 27 cm respectively. From c to d: normalisingthe profiles measured at depths 1.5 cm, 15 cm, 21 cm and 27 cm, each to its correspondingvalue of D1.5, D15, D21 or D27 respectively. From e to f : normalising the simulated profileto E9, which is the vertical-axis value on the central beam axis at depth 9.0 cm.
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CHAPTER 4. SIMULATION OF LINAC SOURCES 46
- that due to the random nature of transport in the phantom, detector and air;
- that due to statistical fluctuation, termed latent variance by Sempau et al.
[2001], in the phase space source.
Uncertainty for the quantity scored (X) was calculated using the standard error
formula:
sX =
√√√√∑N
i=1(Xi −X)2
N(N − 1)(4.1)
where Xi is the X value for the ith independent history, X is the mean value of X
and N is the number of independent histories [Walters et al. 2002]. Here, the author
emphasises independent histories because the definition of a history requires caution,
as will be explained in the next two paragraphs.
A phase space file typically contains data for millions of particles∗. However, not
all particles constitute an independent history. This is because some particles are
correlated, e.g. secondaries originating from the same electron impinging on the linac
target. To account for correlation between such particles, uncertainty estimation
should regard the correlating particles as belonging to the same independent history.
The number of phase space particles (serving as incident source) required for a
particular simulation depends on the geometry setup, volume of the tally and the
desired level of (un)certainty. Since terabytes† of phase space files are impractical
under normal circumstances, particles in a phase space file are sometimes reused in
order to achieve a smaller uncertainty, sX . Each time a particle is reused, it would
∗Every gigabyte contains data for 30 million particles.†1 terabyte = 1012 bytes = 103 gigabytes.
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CHAPTER 4. SIMULATION OF LINAC SOURCES 47
have the same initial position, energy and direction – but tracks a different trajectory
due to random sampling of transport and interaction. Whenever a particle is reused,
all tracks should be regarded as belonging to the same independent history [Walters
et al. 2002]. This is to avoid any underestimation of uncertainties, so that when
particles are heavily reused, the calculated uncertainty would not approach zero, but
a finite value which reflects the latent variance [Sempau et al. 2001] of the phase
space source. In BEAMnrc nomenclature, reusing particles by accounting for such
correlation is called recycling; whereas reusing without accounting for such correlation
is called restarting – which should generally be avoided.
The author has modified and recompiled the original DOSXYZnrc code so that
the code automatically calculates the number of histories according to the desired
number of recycles. This modification eliminates:
- potential undersampling of a phase space file; and
- accidental restarts
which happen e.g. when the number of histories requested by the user is not exact
multiples of the number of particles in the phase space file.
This section sets out to investigate the effects on the tally (T) and the correspond-
ing uncertainty (U) when 1) increasing number of phase space particles are used; and
when 2) phase space particles are recycled. The irradiation setup was a beam inci-
dent on a scanning liquid ionisation chamber (SLIC) electronic portal imager (EPID)
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CHAPTER 4. SIMULATION OF LINAC SOURCES 48
positioned at SDD∗ 140 cm. On the central axis, in the active detection layer†, a
voxel of area 1.6 cm × 1.6 cm was defined as the tally.
The phase space for a 15 cm × 15 cm field produced in Section 4.2.4 (where
the variance reduction techniques bremsstrahlung splitting and Russian roulette were
exercised) were used as the incident beam. Simulations were performed for varying
1) N, phase space particles, ranging from 8 million to 255 million; and 2) R, repeat
cycles, ranging from 0 to 128.
Investigation of the variation of T and U as a function of R was repeated: 1)
without simulating charged particles from the phase space file; 2) with a phase space
file regenerated without bremsstrahlung splitting; and 3) with a phase space file
regenerated with bremsstrahlung splitting but without Russian roulette.
4.3 Results & Discussion
4.3.1 Migration from BEAM00 to BEAMnrc
Photon fluence produced with BEAM00 was found to differ from that produced with
BEAMnrc by more than 5% (Figure 4.4). This suggests the need for recommissioning
MC linac models when migrating to BEAMnrc. It, however, does not imply that
previous simulations using BEAM00 were wrong – since the difference would have
been accounted for in the model-tuning and calibration processes.
∗The SDD has been defined in Figure 2.6.†The active detection layer is the layer containing iso-octane, which has been introduced in
Section 2.3.
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CHAPTER 4. SIMULATION OF LINAC SOURCES 49
1 2 3 4 5 6position (cm)
0
1×10-4
2×10-4
3×10-4
fluence (cm-2)
BEAM00BEAMnrc
Figure 4.4: BEAM00 vs. BEAMnrc: fluence of phase space particles.
4.3.2 Selection of Transport Options
For BEAMnrc simulation of the linac and with the terminology defined in Sec-
tion 4.2.2, configuration B (default) was found to differ significantly from configu-
ration A (first-class). Configuration B over-estimated the energy fluence by 4%. It
also over-estimated the energy spectrum by 7% at the peak (Figure 4.5). Configu-
ration C (optimised) produced phase space characteristics in good agreement with
configuration A (Figure 4.5), while increasing the efficiency over 200 times. Con-
figuration C was therefore adopted for subsequent simulations in the sections which
follow.
Furthermore, it was suspected that the difference between configurations A and
B would diminish when each of the energy fluence and energy spectrum curves were
normalised to its own central axis value. In that case, the difference would have been
corrected by appropriate calibration for subsequent applications. Self-normalisation
was thus carried out, as shown in the bottom panel of Figure 4.5. The difference
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CHAPTER 4. SIMULATION OF LINAC SOURCES 50
0.0 0.5 1.0 1.5 2.0position (cm)
0.0
0.2
0.4
0.6
0.8
1.0
relative energy fluenceA
BC
0 1 2 3 4 5 6energy (MeV)
0.0
0.4
0.8
1.2
population
ABC
0.0 0.5 1.0 1.5 2.0position (cm)
0.0
0.2
0.4
0.6
0.8
1.0
relative energy fluenceA
BC
0 1 2 3 4 5 6energy (MeV)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
population
ABC
Figure 4.5: Energy fluence (left) and energy spectrum (right) of phase space parti-cles scored for configurations A, B and C. Plots before (top) and after (bottom) self-normalisation are shown.
between configurations A and B was found to be smaller but remained significant by
3% at the peak of the energy spectrum.
From DOSXYZnrc simulations of dose deposition in a water phantom, however,
radiation profiles exhibited no noticeable difference. This observation proves that
direct analysis of phase space particles (e.g. fluence and spectrum, as done in this
work) is a more sensitive test than dose deposition in a water phantom, which has
been the reference conventionally adopted by the radiotherapy community.
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CHAPTER 4. SIMULATION OF LINAC SOURCES 51
4.3.3 Fine-tuning the Linac Model
Figure 4.6 and Figure 4.7 show the effects of varying source energy and source radius
on the depth dose and radiation profile respectively. The depth dose is more sensitive
to the source energy, compared to the profile. The profile is more sensitive to the
source radius, compared to the depth dose, as one would expect from geometrical
considerations. The smaller the source radius, the sharper the field penumbra. The
optimal model was found to be a 1.0 mm radius parallel beam of 6.0 MeV electrons.
1 2 3depth (cm)
1.2
1.3
1.4
1.5
relative dose
5.85 MeV5.95 MeV6.10 MeVmeasurement
Figure 4.6: Influence of the incident electron energy on the water phantom depth dose.Data shown is from a simulation of a 5 cm × 5 cm field with 1.5 mm source radius.
4.3.4 Modelling Varying Field Sizes
For square field sizes of side 2 cm, 5 cm, 10 cm, 15 cm, 20 cm and 25 cm, depth
doses and profiles of various field sizes were found to be in good agreement with
measured beam data (Figure 4.8 to Figure 4.13). Except in regions of high dose
gradient within the penumbra, differences between simulation results and measured
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CHAPTER 4. SIMULATION OF LINAC SOURCES 52
0 1 2 3 4position (cm)
0.0
0.5
1.0
1.5
relative dose
0.5 mm1.5 mm2.5 mmmeasurement
Figure 4.7: Influence of the radius of electron source on the radiation profile at 2.5 cmdepth in water. Data shown is from a simulation of a 5 cm × 5 cm field with 5.95 MeVincident electron energy.
data were well within 2% of the central axis value of each radiation profile. Gamma
analysis (explained in the next paragraph) found over 80% of all points fulfilling a 3%-
or-3 mm criterion. Therefore, the single fine-tuned model was found to be universally
applicable to the range of field sizes tested.
The gamma analysis [Low et al. 1998] unifies dose distribution comparisons of
measured and calculated dose distributions. The measure of acceptability is the
difference between the measurement and calculation points in both the dose and the
physical distance, scaled as a fraction of the acceptance criterion.
4.3.5 Use of Phase Space Particles
Surprisingly, increasing R did not monotonically decrease the uncertainty. Fig-
ure 4.14a shows occurrences of such anomalies. The anomalies persisted even when
the experiment was repeated with a much higher number (255 million) of phase space
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CHAPTER 4. SIMULATION OF LINAC SOURCES 53
0 1 2position (cm)
0.0
0.5
1.0
1.5
dose (normalised)
0 1 2position (cm)
-10
-8
-6
-4
-2
0
2
difference (%)
Figure 4.8: Dose profiles in a water tank for a 2 cm × 2 cm beam: measured beam data(lines) and MC simulation results (symbols).
particles∗ (Figure 4.14b). For all graphs presented under this section, T has been
normalised to Tm, which is the value of T when N = 255 million and R = 128, which
are maxima of the tested range.
The top left panel of Figure 4.15 shows the variation in T as a function of R and
N. The bottom left panel displays the same data, but with a binary pass-fail criterion.
The criterion was whether T differed from Tm above (exclusive) or below (inclusive)
∗A phase space file containing 255 million particles occupies 8 gigabytes of disk space.
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CHAPTER 4. SIMULATION OF LINAC SOURCES 54
0 1 2 3 4 5position (cm)
0.0
0.5
1.0
1.5
dose (normalised)
0 1 2 3 4 5position (cm)
-8
-6
-4
-2
0
2
difference (%)
Figure 4.9: Dose profiles in a water tank for a 5 cm × 5 cm beam: measured beam data(lines) and MC simulation results (symbols).
the 0.5% threshold. The top right panel of Figure 4.15 shows the variation in U as a
function of both R and N. The bottom right panel displays the same data, but with a
binary pass-fail criterion. The criterion was whether U was over (exclusive) or under
(inclusive) 0.5%.
In both vertical (R) and horizontal (N) directions, Figure 4.15 shows repeated
occurrences of the anomalies. Although the bottom right corners (corresponding to
high N and high R) of the 4 maps demonstrated a majority passing the pass-fail
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CHAPTER 4. SIMULATION OF LINAC SOURCES 55
0 2 4 6 8 10position (cm)
0.0
0.5
1.0
1.5
dose (normalised)
0 2 4 6 8 10position (cm)
-10
-8
-6
-4
-2
0
2
difference (%)
Figure 4.10: Dose profiles in a water tank for a 10 cm × 10 cm beam: measured beamdata (lines) and MC simulation results (symbols).
criterion, fluctuations persisted. From the 4 maps, it is difficult to judge how large N
and R should be, to be considered adequate for a particular calculation since the trend
is not completely predictable. In theory, increasing R should decrease the numerator
while maintaining the denominator in Equation (4.1); increasing N should increase
the denominator in the same equation. Therefore, in statistical terms, provided the
sample is representative of the population, increasing R and N should each 1) stabilise
T; and 2) decrease U. The anomalies, therefore, required further investigation.
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CHAPTER 4. SIMULATION OF LINAC SOURCES 56
0 5 10position (cm)
0.0
0.5
1.0
1.5
dose (normalised)
0 5 10position (cm)
-5
-4
-3
-2
-1
0
1
2
difference (%)
Figure 4.11: Dose profiles in a water tank for a 15 cm × 15 cm beam: measured beamdata (lines) and MC simulation results (symbols).
When the experiment was repeated without simulating charged particles from the
phase space file, the uncertainty decreased monotonically with increasing number of
recycles (Figure 4.16a). In other words, the anomalies disappeared.
This led to the suspicion that the phase space file used somehow contained an
inadequate representation of electrons. This prompted regeneration of a phase space
file without using bremsstrahlung splitting. With the regenerated phase space file,
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CHAPTER 4. SIMULATION OF LINAC SOURCES 57
0 5 10 15position (cm)
0.0
0.5
1.0
1.5
dose (normalised)
0 5 10 15position (cm)
-6
-4
-2
0
2
difference (%)
Figure 4.12: Dose profiles in a water tank for a 20 cm × 20 cm beam: measured beamdata (lines) and MC simulation results (symbols).
repetition of the experiment showed monotonic decrease of U with increasing number
of R, i.e. the anomalies disappeared (Figure 4.16b). The anomalies also disappeared
in a further test using a phase space file regenerated using bremsstrahlung splitting
but without Russian roulette (Figure 4.16c).
Additionally, it can be observed from Figure 4.16 that when bremsstrahlung split-
ting was used, U decreased slower with increasing R – which is expected since variance
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CHAPTER 4. SIMULATION OF LINAC SOURCES 58
0 5 10 15 20position (cm)
0.0
0.5
1.0
1.5
dose (normalised)
0 5 10 15 20position (cm)
-4
-2
0
2
4
6
difference (%)
Figure 4.13: Dose profiles in a water tank for a 25 cm × 25 cm beam: measured beamdata (lines) and MC simulation results (symbols).
reduction techniques create pseudo-particles, as opposed to truly, statistically, inde-
pendent particles created using an analog transport.
Results confirmed that indeed the variance reduction regime combining bremsstrah-
lung splitting and Russian roulette produced inadequate representation of electrons.
However, the difference it causes in T is no more than 2% (when 255 million particles
were used), since the electron contribution to photon beams (which is of interest in
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CHAPTER 4. SIMULATION OF LINAC SOURCES 59
this thesis) is merely as a contaminant. That said, the combination of bremsstrahlung
splitting and Russian roulette is not recommended for BEAMnrc simulations of the
linac head. For future work, the recently implemented directional bremsstrahlung
splitting [Kawrakow et al. 2004], which was designed not only to increase efficiency
but also to overcome the under-representation of electrons, should instead be used.
0 20 40 60 80 100 1200.90
0.95
1.00
1.05
1.10
1.15
T
255,373,320 photons and charged particles
0 20 40 60 80 100 1200.90
0.95
1.00
1.05
1.10
1.15
T
8,512,980 photons and charged particles
0 20 40 60 80 100 120R
0
2
4
6
8
U
0 20 40 60 80 100 120R
0
2
4
6
8
U
ba
Figure 4.14: T (tally) and U (the corresponding percentage uncertainty) as a functionof R (number of recycles) when a) 8,512,980; and b) 255,373,320 phase space photons andcharged particles were simulated.
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CHAPTER 4. SIMULATION OF LINAC SOURCES 60
NUMBER OF PARTICLES
NU
MB
ER
OF
RE
CY
CL
ES
0.5 1 1.5 2 2.5
x 108
30
40
50
60
70
80
90
100
110
120
1300.97
0.975
0.98
0.985
0.99
0.995
1
1.005
1.01
1.015
NUMBER OF PARTICLES
NU
MB
ER
OF
RE
CY
CL
ES
0.5 1 1.5 2 2.5
x 108
30
40
50
60
70
80
90
100
110
120
130−0.6
−0.4
−0.2
0
0.2
0.4
0.6
NUMBER OF PARTICLES
NU
MB
ER
OF
RE
CY
CL
ES
0.5 1 1.5 2 2.5
x 108
30
40
50
60
70
80
90
100
110
120
130
NUMBER OF PARTICLES
NU
MB
ER
OF
RE
CY
CL
ES
0.5 1 1.5 2 2.5
x 108
30
40
50
60
70
80
90
100
110
120
130
Figure 4.15: Top left: T (tally), normalised to Tm, as a function of R (number of recycles)and N (number of phase space particles). Bottom left: instances of T differing from Tm byless than 0.5% (black) and those over 0.5% (white). Top right: percentage of U (uncertainty)as a function of R and N, grayscale given in log10 scale. Bottom right: instances of U below0.5% (black) and those over 0.5% (white).
4.4 Conclusions
The new BEAM version, BEAMnrc, was found to produce different simulation out-
comes compared to its predecessor, BEAM00. The same input files produced photon
fluences which differed by over 5% for the linac simulated here. Our investigations also
indicated substantial differences when first-class transport made available by BEAM-
nrc was used in place of the default settings. Although no difference was noticeable
in water phantom dose deposition, energy fluence and energy spectra of the phase
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CHAPTER 4. SIMULATION OF LINAC SOURCES 61
space particles differed up to 4% and 7% respectively. Our findings also confirmed
insensitivity of water phantom dose deposition for analysing phase space particles,
i.e. dose deposition in a water phantom is inadequate for benchmarking transport
configurations for MC simulations. Instead, direct analysis of phase space particles
(e.g. energy fluence and energy spectra) are recommended.
In BEAMnrc simulation of the linac, the combination of bremsstrahlung split-
ting and Russian roulette variance reduction techniques was found to cause peculiar
statistical fluctuations, due to under-representation of contaminant electrons. The
author proposes a new method for qualifying that a phase space is an adequately
representative sample of a beam – by monitoring the uncertainty as a function of
increasing number of particles and number of repeat cycles, as used to investigate the
aforementioned anomalies.
The fine-tuned linac model was found to be a 1.0 mm radius parallel beam of
6.00 MeV electrons. The beam radius is in agreement with the range found from
measurements by Jaffray et al. [1993], while the incident energy is in exact agreement
with the definition of the linac energy mode, although this is only nominal.
The same linac model was found to be universally applicable for field sizes ranging
from 2 cm × 2 cm to 25 cm × 25 cm. When simulated to tally dose deposition in a
water tank, dose distributions were within 2% (of the central axis dose at each depth)
agreement with measured beam data, except in the penumbra region of high dose
gradients.
This outcome equips our data library with fully commissioned phase space files for
2 cm × 2 cm, 5 cm × 5 cm, 10 cm × 10 cm, 15 cm × 15 cm, 20 cm × 20 cm and 25
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CHAPTER 4. SIMULATION OF LINAC SOURCES 62
cm × 25 cm beams. These can be readily deployed for MC simulations of various dose
calculations over a wide range of source-phantom-EPID setups e.g. various gantry
angles, source-surface and source-detector distances. Repeated simulations of the
linac head would not be necessary since 1) changing the source-phantom-EPID setup
does not change the arrangement of the target, primary collimators, vacuum window,
flattening filter, monitor ion chamber and mirror within the linac head; and 2) the
phase space files were generated at a plane upstream from probable locations of the
phantom/patient.
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CHAPTER 4. SIMULATION OF LINAC SOURCES 63
60 80 100 120
0.96
0.98
1.00
1.02
1.04
T
8,498,710 photons and charged particles
60 80 100 120R
0.0
0.2
0.4
0.6
0.8
1.0
U
b
60 80 100 120
0.96
0.98
1.00
1.02
1.04
T
9,212,927 photons and charged particles
60 80 100 120R
0.0
0.2
0.4
0.6
0.8
1.0
U
c
60 80 100 120R
0.0
0.2
0.4
0.6
0.8
1.0
U
60 80 100 120
0.96
0.98
1.00
1.02
1.04
T
8,512,900 photons only
a
Figure 4.16: T (tally) and U (the corresponding percentage uncertainty) as a function of R(number of recycles) when a) only photons were simulated; b) phase space particles were re-simulated without bremsstrahlung splitting; and c) phase space particles were re-simulatedwith bremsstrahlung splitting but without Russian roulette.
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Chapter 5
TREATMENT VERIFICATION:
A MONTE CARLO SOLUTION
Advanced external beam radiotherapy techniques involving conformal field shaping
and/or intensity modulation require thorough verification. This chapter reports a
treatment verification solution which combines the accuracy of Monte Carlo (MC)
simulations with the technology of electronic portal imaging devices (EPIDs). Here is
the core of the thesis where the project achieved combined versatility and accuracy
not known to be readily achievable by other verification techniques. The solution
is versatile in that dose prediction has been tested over a wide range of clinical
setups including high scatter conditions which complicate portal dose prediction. It
is accurate in that agreement with measured dose profiles was consistently within
2% of the central axis value.
This was made possible by introducing a modified calibration method, a new way
of simulating oblique beams using DOSXYZnrc, and a correction algorithm for gantry-
dependent EPID response (which is implemented in this chapter but derivation will
be given in Chapter 7).
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CHAPTER 5. A MONTE CARLO SOLUTION 65
5.1 Introduction
The clinical need for dosimetric treatment verification and the limitations of diodes
and thermoluminescent dosimeters (TLDs) have been outlined in Section 1.1. The
role of EPIDs is promising (Section 1.2, Chapter 2). However, existing EPID-based
verification techniques lack versatility and accuracy due to assumptions made in dose
calculations (Section 1.5). MC simulations are known to be the most accurate dose
calculation technique because it makes no presumptions about the scatter condition
in the problem at hand (Chapter 3). Combining the accuracy of MC simulations with
the technology of EPIDs, this thesis developed a versatile and accurate solution for
treatment verification.
The following explains how the solution works. By imaging during beam delivery,
image pixel values were used to derive quantitative data on the dose delivery. This
exercise converts the image to a dose map. This dose map was then compared against
a dose map predicted using MC simulation based on parameters from the treatment
planning system (TPS). A disagreement would indicate that beam delivery had not
been according to plan.
This solution extends an existing MC verification framework developed within the
same institution, which verifies TPS-calculated patient dose against MC simulations.
The complete MC verification framework is outlined in Figure 5.1: VERIFICATION
1 has been developed by Spezi ([Spezi 2003]), VERIFICATIONS 2 & 3 are the au-
thor’s contribution. Measured images are first calibrated for dose and corrected for
off-axis variations (detailed in Section 5.2.1.2 and Section 5.2.1.3 respectively). Cor-
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CHAPTER 5. A MONTE CARLO SOLUTION 66
SIMULATED DOSE MAGE SIMULATED PATIENT DOSE
CT SCAN DATASET
SOURCE−PATIENT−EPID GEOMETRY
BEAMnrc & DOSXYZnrc
DICOM−RT TOOLBOX + TWIZ&GLU
TPS DOSE CALCULATION
FIELD & DOSIMETRIC SETTINGS
OFF−AXIS CORRECTION
GANTRY EFFECTS CORRECTION
IRRADIATION
MEASURED DOSE IMAGE
GRAYSCALE−TO−DOSE CALIBRATION
MEASURED IMAGE
VERIFICATION 1
VERIFICATIONS 2 & 3
Figure 5.1: A MC verification framework: 1. verifying TPS dose calculation; 2. verifyingimplementation of TPS-generated parameters on treatment machine; 3. verifying patientdose delivery. Steps in the dashed box are repeated for subsequent treatment fractions.
rection for gantry effects is needed for SLIC-type EPIDs since its response varies with
gantry angle, causing an artefact commonly known as the bulging effect (detailed in
Section 7.2.1). An identical irradiation configuration would be MC-simulated. Sec-
tion 5.2.3 demonstrates the use of this solution to predict portal images from a SLIC
EPID over a wide range of clinical setups.
5.2 Materials and Methods
We used a Varian Clinac 2100CD linac installed with a PortalVision Mk2 SLIC EPID
supported by a retractable arm (R-arm). It produces portal images of 256×256 pixels,
where each square pixel is 1.27 mm in dimension, giving a 32.5 cm × 32.5 cm image
area.
The SLIC detector measures dose rate but not cumulative dose [Essers et al. 1995].
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CHAPTER 5. A MONTE CARLO SOLUTION 67
Since the electronic portal images (EPIs) were acquired at approximately constant
dose rates, the detector signal, and hence the image grayscale, may be assumed to be
a measure of dose.
In sections where EPIs were predicted, the SLIC EPID was modelled in detail as
specified by the manufacturer. DOSXYZnrc was used to predict dose deposition in
each voxel on the EPID’s active detection layer∗. The radiation source was provided
by the phase space library produced in Chapter 4.
5.2.1 Calibrations
5.2.1.1 Image Calibration
For image calibration, standard dark field (DF) and flood field (FF) calibration was
applied [Essers et al. 1995]. A dark field, acquired with beam off, accounts for cham-
ber imperfections, electrical leakage and high-voltage switching artefacts. A flood
field, acquired with an open radiation field covering the detector area, accounts for
individual cell sensitivities and electrometer gains.
We performed the calibration at SDD† 140 cm and gantry angle 0◦ without plac-
ing any object in the beam. An image was acquired immediately after calibration
using the same setup as that used for calibration. Uniformity of this image gave an
indication of calibration validity. For this purpose, image matrix I0 was compared
with the (scalar) central axis value C0. The uniformity matrix was calculated as
U =I0 − C0
C0
(5.1)
∗The active detection layer is the layer containing iso-octane.†The SDD has been defined in Figure 2.6.
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CHAPTER 5. A MONTE CARLO SOLUTION 68
5.2.1.2 Grayscale-to-dose Calibration
Before an EPI could be interpreted as a dose map, a grayscale-to-dose calibration
is needed. The calibration function, once established, can be used for converting
subsequent EPIs into dose maps. To construct the calibration function, matching
pairs of grayscale and dose values are required across the desired calibration range.
Our calibration function was constructed by relating physically-acquired grayscales
to MC-simulated doses. EPIs were physically acquired for varying beam sizes (5 cm
× 5 cm to 20 cm × 20 cm), perspex phantom thicknesses (0 cm to 20 cm) and SDDs
(105 cm to 140 cm) so that a range of effective doses incident on the detector could
be obtained. The gantry angle was kept at 0◦. For each physically-acquired EPI, the
same irradiation condition was simulated to produce a corresponding MC-simulated
dose map.
Matching pairs of grayscale and dose values were extracted from the physically-
acquired EPI and the corresponding MC-simulated dose map respectively. Values
were averaged over a 1 cm × 1 cm area at the centre of the EPI and the dose map,
which corresponds to the beam central axis.
The grayscale G (dimensionless) and dose D (in units of Gray per incident particle
history) values obtained were curve-fitted using regression model I:
G = α√
D (5.2)
and model II:
G = αD + β√
D + γ (5.3)
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CHAPTER 5. A MONTE CARLO SOLUTION 69
where α, β and γ are the regression coefficients. Model I is the square-root response
function commonly used (e.g. Spezi and Lewis [2002]) as an approximation to model
II, which has been derived theoretically [Essers et al. 1995]. The models were evalu-
ated for applicability across different dose levels.
5.2.1.3 Off-axis Calibration
As mentioned earlier, DF/FF calibration was performed without placing any object
in the field. Consequently, images of the same setup calibrated this way would be
uniform, therefore losing the unflatness or horns due to the flattening filter. To offset
this effect, an off-axis calibration is needed. We restore the horns by analysing a
dose map from MC-simulation of an irradiation condition identical to that during FF
calibration, that is, a 25 cm square field incident on the EPID at SDD 140 cm.
From this MC-simulated dose map, an off-axis-ratio map was derived by dividing
the value of each pixel by that of the central axis. This off-axis-ratio map was modelled
in two ways:
1. the square-ring method [Spezi and Lewis 2002]. Starting from the central axis
(CAX), pixels were grouped into concentric square rings of increasing distance
from the CAX. Regression was done with the value at each pixel as the depen-
dent variable, and the distance of the side of the square ring from the CAX as
the independent variable.
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CHAPTER 5. A MONTE CARLO SOLUTION 70
2. the radial distance method, where regression was done with the value at each
pixel as the dependent variable, and the distance of the pixel centre from the
CAX as the independent variable.
The models were analysed by calculating the difference from the original off-axis-ratio
map.
5.2.2 Phantom Packaging Using TWIZ&GLU
MC simulation of portal dosimetry requires both the phantom and the imager to
be modelled. At gantry angles of 0◦ (Figure 5.2a), 90◦ and 270◦, voxel boundaries
directly correspond to phantom and imager surfaces. At an oblique angle, however,
the voxel boundaries no longer directly correspond to imager surfaces (Figure 5.2b).
DOSXYZnrc [Walters and Rogers 2002] is frequently used for dose simulation in
a phantom. The geometry is specified on a set of orthogonal planes. These planes
form a 3D lattice of voxels where each voxel is assigned a material and a density.
Consequently, accurate specification of voxel boundaries not directly corresponding
to imager surfaces (as happens in portal dosimetry of oblique beams, explained in
the previous paragraph) is problematic. Whereas DOSXYZnrc allows the beam to
be directed onto the voxel grid from any gantry angle, it was not designed to model
objects with planes oriented obliquely to each other within the voxel grid. We there-
fore developed a MATLAB∗ script for packaging an integrated phantom to serve as
input for DOSXYZnrc simulations. With this, we present a variable angle solution
∗A language of technical computing. The website is at www.mathworks.com.
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CHAPTER 5. A MONTE CARLO SOLUTION 71
*
a) b)*
I
S
S
P
Figure 5.2: Defining a patient/phantom dataset (P) and an imager (I) on a commonrectilinear grid. Beam direction from the source (S) is shown: a) irradiation from gantryangle of 0◦; b) irradiation from an oblique angle, where the voxel boundaries no longerdirectly correspond to the imager surfaces (dashed box).
for MC simulation of phantom-imager geometries.
For simulation of portal dosimetry at gantry angle of θ◦ (Figure 5.3a), the script
we developed (TWIZ&GLU) operated on the patient/phantom CT dataset in three
steps: 1) rotating the phantom by -θ◦ around the isocentre (Figure 5.3b); 2) “padding”
the exterior of the phantom with additional air-filled voxels to obtain a rectangular
frame (Figure 5.3c); and 3) adding the EPID beneath the phantom at a specified
SDD (Figure 5.3d). The integrated phantom was then ready to serve as input for a
DOSXYZnrc run, in which the beam was directed as if the gantry was not rotated.
The phantom file was produced in ASCII format, similar to that used in DOSXYZ-
nrc. However, the author introduced a new material indexing convention. In DOSXYZ-
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CHAPTER 5. A MONTE CARLO SOLUTION 72
AIR
c)
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− θ
INTEGRATEDPHANTOM
d)
b)
���������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������
���������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������
θ
a)
Figure 5.3: a) The task of modelling a phantom-imager geometry for irradiation at gantryangle of θ◦. TWIZ&GLU operated in three steps: b) rotating the phantom by -θ◦ aroundthe isocentre; c) ”padding” the exterior of the phantom with additional air-filled voxels; d)adding the EPID downstream from the phantom at a specified SDD. The beam directionis shown.
nrc, each material in a CT phantom is indexed using a single digit ranging from one
to nine. This limits the phantom composition to a maximum of 9 materials, which
is insufficient for the integrated phantoms developed in this work. By incorporating
characters and symbols from the ASCII map, our new indexing convention extended
the limit to over 200 materials. DOSXYZnrc was similarly modified for compatibility.
Rotation, resolution resampling and discretisation from continuous contours into
pixel-defined contours may cause distortions, asymmetries and artefacts. Some of
these are illustrated in Figure 5.4. S1 is a result of rotation of a straight-sided square.
The sides became stepped, demonstrating step artefacts. Also shown is S2 which joins
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CHAPTER 5. A MONTE CARLO SOLUTION 73
the centres of each vertex pixel. S3 is the location of S2 after a 90◦ rotation. The
non-overlapping of S2 and S3 shows that the right-angled corners were not faithfully
reproduced. More extensive deviations will occur when a larger pixel size is used.
S
S
S1
2
3
Figure 5.4: S1 is a result of the rotation of a straight-sided square. The sides are steppedand the corners are not truly right angles. S2 (solid line) joins the centre of each vertexpixel. S3 (dashed line) is the location of S2 after a 90◦ rotation.
With these concerns in mind, we tested the accuracy of geometric transformations
by TWIZ&GLU. This was done using trigonometric calculations on the rotation of
a 10 cm × 10 cm square. Reproducibility of the length of each side, reproducibility
of the geometric centre, and the accuracy of rotation angles were tested for rotation
angles in steps of 10◦ over the entire circle. The length of each side and the angle of
rotation were calculated trigonometrically from the coordinates of the centre of each
vertex pixel. Verification of the geometric transformation algorithm was repeated for
pixel sizes 2 mm, 2.5 mm, 3 mm and 4 mm.
Upon completing technical tests on the geometric transformations, we investigated
the implementation of the integrated phantom method for MC simulations. Two
independent MC computations of portal dose were performed on a 10 cm × 10 cm
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CHAPTER 5. A MONTE CARLO SOLUTION 74
× 10 cm water phantom irradiated at gantry angle of 45◦, source-axis distance 100
cm and SDD 140 cm: 1) a conventional BEAMnrc run on a cubic phantom followed
by a DOSXYZnrc run for scoring portal dose (Figure 5.5a and c). Here, the CM∗
pyramids was used to generate two wedge shapes arranged to form a cubic phantom.
2) a DOSXYZnrc run on a TWIZ&GLU-generated phantom consisting of a cube
rotated by 45◦ and an EPID (Figure 5.5b and c). Cubic phantoms in both cases were
identical. Dose profiles were then compared.
All simulations in this section used a 6 MV, 10 cm × 10 cm accelerator source
phase space file, as detailed in Chapter 4.
TWIZ&GLU
+
=
45
EPID
a) b) c)
Figure 5.5: Identical phantoms generated using a) pyramids CM from BEAMnrc; b)TWIZ&GLU by rotating a cube over 45◦; c) MC simulation of phantom irradiation forportal dosimetry.
Finally, we demonstrated an application of the newly developed solution for portal
dose prediction. An EPI was taken for oblique beam irradiation of an inhomogeneous
solid water phantom. This was compared with a MC simulation performed under
∗Component modules (CMs) have been introduced in Section 3.4.
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CHAPTER 5. A MONTE CARLO SOLUTION 75
identical conditions. Shown in Figure 5.6, the 30 cm × 30 cm × 18 cm water phantom
with an embedded 4 cm × 30 cm × 2 cm air gap was irradiated at gantry angle of
20◦ by a 10 cm × 10 cm 6 MV photon beam, SSD∗ 90 cm and SDD 140 cm.
2cm
30cm
30cm
4cm30cm18cm
Figure 5.6: A solid water phantom with an air gap at the centre.
5.2.3 Demonstrations
To test the verification chain developed (Figure 5.1), 15 cm × 15 cm perspex slabs
of 1 cm, 2 cm and 2.5 cm thick were constructed in-house by the physics workshop.
Additionally, some slabs were constructed with a 5 cm × 5 cm cutout at the centre. A
base plate of the same material extends beyond the couch to support the slabs. This
way, the couch could be kept out of the imaged beam. EPIs were physically-acquired
and MC-predicted for varying:
- field sizes (5 cm, 10 cm, 15 cm and 20 cm square fields)
- phantom-EPID air gap distance† (4 cm, 28 cm and 38 cm)
∗The SSD has been defined in Figure 2.6.†The air gap distance has been defined in Figure 2.6.
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CHAPTER 5. A MONTE CARLO SOLUTION 76
- gantry angles (20◦, 140◦, 240◦ and 280◦ as representative samples across all 4
quadrants at varying tilt from the vertical)
The 4 cm gap value was the minimum phantom-EPID separation achievable without
collision between the EPID and the couch. This minimum separation was close to
provide a high radiation scatter component as a stringent test condition.
Using the calibration function of model II and the radial distance method for
off-axis calibration, dose profiles were extracted from the EPIs and the dose maps.
5.3 Results & Discussion
5.3.1 Calibrations
5.3.1.1 Image Calibration
0.000 0.005 0.010 0.015 0.020uniformity (fraction)
0.0
0.2
0.4
0.6
0.8
1.0
population (normalised)
calibration not updatedcalibration updated
Figure 5.7: Cumulative histograms for image uniformity of two images: one acquiredduring a session which began with a calibration update; another acquired on a day whenthe most recent calibration update was a fortnight earlier.
To check the validity of DF/FF calibration, each pixel of I0 was compared with
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CHAPTER 5. A MONTE CARLO SOLUTION 77
C0. A cumulative histogram of uniformity as defined in Equation (5.1) is shown in
Figure 5.7 for two images: one acquired during a session which began with a cali-
bration update; another acquired on a day when the most recent calibration update
was a fortnight earlier. Results indicated the importance of calibration updates in
dosimetric work. When the calibration was not updated during the same session,
only 87% of the pixels achieved 1% uniformity. However, when the calibration was
updated at the start of the session, uniformity was very good, with 99% of the pixels
uniform within 1%.
5.3.1.2 Grayscale-to-dose Calibration
0.0e+00 5.0e-17 1.0e-16Gy per incident particle
0
2000
4000
6000
8000
grayscale
Figure 5.8: Grayscale-to-dose calibration: physically-acquired grayscales on the verticalaxis and MC-simulated dose values on the horizontal axis (dots). Also shown are the regres-sion models I (dashed curve) and II (continuous curve), and the data point correspondingto the previously tested limit (straight lines).
Curve-fitting results for grayscale-to-dose calibration are shown in Figure 5.8.
Model I fits well up to the previously tested limit (marked on figure), which is a 10
cm square field without any object placed in the beam at SDD 140 cm [Spezi and
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CHAPTER 5. A MONTE CARLO SOLUTION 78
Lewis 2002]. It, however, overestimates the dose at regions of higher dose. Model II
fits better over the entire tested range. The coefficients found for model II were α =
100.5, β = 2136 and γ = 25.79. Our findings confirm the increasing significance of α
as the dose increases [Essers et al. 1995].
This calibration method, where dose values for the horizontal axis of the cali-
bration curve (Figure 5.8) are derived from MC simulations, is more accurate than
other methods [Boellaard et al. 1996, McNutt et al. 1996, van Esch et al. 2001, 2004,
Vieira et al. 2004], where dose values are obtained from ion chamber measurements
in a water phantom. A comparison of these two calibration methods will be given in
Chapter 6.
5.3.1.3 Off-axis Calibration
From the MC-simulated dose map for a 25 cm square field at SDD 140 cm, the off-axis-
ratio map was calculated (Figure 5.9 A) and modelled using the square-ring and the
radial distance methods. Off-axis-ratio maps produced from the models (Figure 5.9 B
and C) were analysed by calculating the difference from the original (Figure 5.9 D and
E). The square-ring method produced an X-shape artefact, particularly noticeable at
large field sizes. The radial distance model is more accurate since the flattening filter
has circular, not square, symmetry. And it is the flattening filter which shapes the
off-axis effects that we are trying to model. The radial distance model produced the
following relation for off-axis calibration:
OAR = 1.298× 10−5r3 − 5.536× 10−4r2 + 0.0098r + 0.9937 (5.4)
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CHAPTER 5. A MONTE CARLO SOLUTION 79
1
1.02
1.04
1.06
1.08
1.1
−4
−2
0
2
B C
ED
A
%
Figure 5.9: Off-axis calibration: off-axis-ratio maps from (A) the original dose map; (B)the square-ring model; and (C) the radial distance model. (D) difference between A and B,where an X-shape artefact is visible. (E) difference between A and C.
where OAR is the off-axis-ratio and r is the distance from the central axis in centime-
tres.
5.3.2 Phantom Packaging Using TWIZ&GLU
As illustrated in Figure 5.4, TWIZ&GLU was tested for spatial shift and angular
deviation. The length of each side of the rotated square was found to deviate from
that calculated trigonometrically by less than a single pixel size. A similar degree of
uncertainty was observed for the reproducibility of the geometric centre. The rotation
angle measured deviated from its true value by less than 1◦ for a 2 mm pixel size,
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CHAPTER 5. A MONTE CARLO SOLUTION 80
−8 −6 −4 −2 0 2 4 6 80
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5x 10
−17
x/cm
dose
per
inci
dent
par
ticle
/Gy
Cube
2 mm4 mmBEAMnrc
Figure 5.10: Crossplane profiles of cubes irradiated at gantry angle of 20◦, for comparingintegrated phantoms of pixel sizes 2 mm and 4 mm with pyramids CMs of BEAMnrc.
and less than 2◦ for a 4 mm pixel size.
These findings confirmed successful implementation of the integrated phantom
method for MC simulations. As shown in Figure 5.10, good agreement was found be-
tween dose profiles of two identical geometries produced independently (Figure 5.5):
one using the CMs from BEAMnrc, another using the integrated phantom from
TWIZ&GLU. Figure 5.10 also shows that step artefacts caused no detrimental im-
pact. No significant loss of accuracy was observed from 4 mm pixel size.
Finally, portal dose prediction of a solid water slab embedded with an air gap
irradiated at gantry angle of 20◦ was compared with measurements. The agreement
was good throughout (Figure 5.11) with a root-mean-square of the difference below
2% within the field, confirming the geometry transformation has not compromised
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CHAPTER 5. A MONTE CARLO SOLUTION 81
−8 −6 −4 −2 0 2 4 6 80
0.5
1
1.5
2
2.5
3x 10
−17
x/cm
dose
per
inci
dent
par
ticle
/Gy
Slab
measuredsimulated
Figure 5.11: Crossplane profiles of a solid water phantom embedded with an air gap,irradiated at gantry angle of 20◦.
the accuracy of the simulations.
In constructing an integrated phantom of objects oriented obliquely to each other,
in our case the phantom and the imager, objects were put into a common rectilinear
grid. Our implementation rotated and resampled the phantom in order to correspond
to the orientation of the imager. Alternatively, the imager could be rotated and
resampled into the grid defining the phantom. However, this alternative approach
would lead to inaccurate projection of the different thicknesses of the detector layers
on the grid.
Another alternative to using an integrated phantom would be to simulate each
stage of the process (Figure 5.3) successively. This would require a phase space
output from simulation of the CT phantom, which requires additional disk space and
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CHAPTER 5. A MONTE CARLO SOLUTION 82
is not supported by the current version of DOSXYZnrc.
5.3.3 Demonstrations
Agreement between simulated and measured portal dose profiles was generally within
2% of the central axis dose (Fig. 5.12, 5.13 and 5.14), except in regions of high dose
gradient which are particularly susceptible to positional uncertainties of the measuring
devices and linac jaws during measurements. For all comparisons shown in Fig. 5.12,
5.13 and 5.14, the measured profile has been normalised to the measured portal dose
at SDD 140 cm on the central axis of a 10 cm × 10 cm beam; the predicted profile has
been normalised to the predicted portal dose at the same beam-EPID setup. This
allows absolute dose verification. It should be emphasised that the measured and
predicted profiles were never normalised to each other, as practised elsewhere (e.g.
McCurdy et al. [2001]).
No field size dependence was observed. There was no loss of accuracy 1) in high
scatter conditions when the phantom-to-EPID separation was only 4 cm; 2) with the
presence of a 20 cm cubic perspex phantom, even when a 4 cm-thick, 5 cm × 5 cm
air cavity was introduced at its centre; 3) when the gantry was rotated for delivery of
oblique beams; and 4) in the absence of additional buildup on the EPID. Such inclu-
sive versatility is known to be unachievable in non-MC portal dosimetry [Boellaard
et al. 1997, van Esch et al. 2001, Vieira et al. 2004] as explained in Section 1.5.
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CHAPTER 5. A MONTE CARLO SOLUTION 83
FS 20
FS 15
FS 10
FS 05
0 5 10 15-6
-4
-2
0
2
4
6
0 5 10 150.0
0.2
0.4
0.6
0.8
1.0
dose (normalised)
measured, FS 10predicted, FS 10
0 5 10 15-6
-4
-2
0
2
4
6
difference (%)
0 5 10 150.0
0.2
0.4
0.6
0.8
1.0
dose (normalised)
measured, FS 20predicted, FS 20
0 5 10 15position (cm)
-6
-4
-2
0
2
4
6
difference (%)
0 5 10 150.0
0.2
0.4
0.6
0.8
1.0measured, FS 05predicted, FS 05
0 5 10 150.0
0.2
0.4
0.6
0.8
1.0measured, FS 15predicted, FS 15
0 5 10 15position (cm)
-6
-4
-2
0
2
4
6
Figure 5.12: Irradiation of a homogeneous phantom at 5 cm, 10 cm, 15 cm and 20 cmsquare field sizes: the beam-phantom-EPID setup, the predicted and measured portal doseprofiles, and the corresponding differences. The air gap distance and the gantry angle werefixed at 13 cm and 0◦ respectively.
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CHAPTER 5. A MONTE CARLO SOLUTION 84
4 cm AIR GAP28 cm AIR GAP38 cm AIR GAP
AIR GAP
0 5 10 15position (cm)
-6
-4
-2
0
2
4
6
difference (%)
0 5 10 15
0.2
0.4
0.6
0.8
dose (normalised)
measured, 38 cm gappredicted, 38 cm gap
0 5 10 15position (cm)
-6
-4
-2
0
2
4
6
difference (%)
0 5 10 15
0.2
0.4
0.6
0.8dose (normalised)
measured, 4 cm gappredicted, 4 cm gap
0 5 10 15
0.2
0.4
0.6
0.8 measured, 28 cm gappredicted, 28 cm gap
0 5 10 15position (cm)
-6
-4
-2
0
2
4
6
Figure 5.13: Irradiation of an inhomogeneous phantom (Figure 5.6) at air gap distances38 cm, 28 cm and 4 cm: the beam-phantom-EPID setup, the predicted and measured portaldose profiles, and the corresponding differences. The field size and the gantry angle werefixed at 15 cm × 15 cm and 0◦ respectively.
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CHAPTER 5. A MONTE CARLO SOLUTION 85
G 20
G 280
G 240
G 140
-15 -10 -5 0 5 10 15
0.2
0.3
0.4
0.5
0.6
measured, G 20predicted, G 20
-15 -10 -5 0 5 10 15
0.2
0.3
0.4
0.5
0.6
dose (normalised)
measured, G 140predicted, G 140
-15 -10 -5 0 5 10 15-6
-4
-2
0
2
4
6
difference (%)
-15 -10 -5 0 5 10 15-6
-4
-2
0
2
4
6
-15 -10 -5 0 5 10 15
0.2
0.3
0.4
0.5
0.6
measured, G 240predicted, G 240
-15 -10 -5 0 5 10 15
0.2
0.3
0.4
0.5
0.6
dose (normalised)
measured, G 280predicted, G 280
-15 -10 -5 0 5 10 15position (cm)
-6
-4
-2
0
2
4
6
-15 -10 -5 0 5 10 15position (cm)
-6
-4
-2
0
2
4
6
difference (%)
Figure 5.14: Isocentric irradiation of an inhomogeneous phantom (Figure 5.6) at gantryangles 20◦, 140◦, 240◦ and 280◦: the beam-phantom-EPID setup, the predicted and mea-sured portal dose profiles, and the corresponding differences. The field size and the SDDwere fixed at 15 cm × 15 cm and 140 cm respectively.
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CHAPTER 5. A MONTE CARLO SOLUTION 86
5.4 Conclusions
This project successfully extended an existing MC calibration method for predicting
SLIC EPIs [Spezi and Lewis 2002], which had been limited to 0◦ gantry angle and 10
cm × 10 cm beams. Now, EPI prediction for beams from 5 cm × 5 cm up to 20 cm
× 20 cm has been validated. The improved method also allows portal dose prediction
of oblique beams, which has not been previously reported.
This was achieved by introducing modified grayscale-to-dose and off-axis cali-
bration methods, a correction algorithm for gantry-dependent artefacts in the SLIC
(detailed in Section 7.2.1), and a novel solution to enable DOSXYZnrc simulations of
portal dosimetry at oblique gantry angles.
TWIZ&GLU has been developed to enable DOSXYZnrc simulations of portal
dosimetry at oblique gantry angles. The solution is based on an integrated phantom,
whereby the effect of incident beam obliquity was included using geometric transfor-
mations. Geometric transformations are accurate within±1 mm and±1◦ with respect
to exact values calculated using trigonometry. As a process independent of the MC
code itself, the TWIZ&GLU solution is compatible across evolving code generations,
e.g. DOSXYZ and DOSXYZnrc.
The versatile MC solution for external beam photon radiotherapy verification has
been validated under a wide range of clinical setups, including high scatter conditions
which complicate portal dose prediction. Off-axis agreement with portal dose profiles
was within 2% of the central axis value. This combined versatility and accuracy is
not readily achievable by other techniques.
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CHAPTER 5. A MONTE CARLO SOLUTION 87
Whereas the examples shown here were based on the SLIC EPID, the MC solution
shown in Figure 5.1 can be readily adapted for the a-Si EPID as follows:
1. replacing the quadratic function in Section 5.2.1.2 with a linear grayscale-to-
dose calibration function (details in Chapter 6), which would be even simpler;
2. employing a similar off-axis calibration method, by deriving new coefficients
based on actual and predicted EPIs of an a-Si EPID;
3. ignoring the corrections for bulging effect (Section 7.2.1), which are irrelevant
for the a-Si EPID as it does not contain liquid;
4. employing the same TWIZ&GLU solution.
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Chapter 6
OPTIMISATION OF MONTE
CARLO SIMULATIONS
The radiation source, the geometry and the transport parameters are important user
inputs to a Monte Carlo (MC) simulation (Figure 1.4). The reliability of simulation
output depends largely on these inputs, i.e. “garbage in, garbage out”. This thesis
includes optimisation of each of these inputs, in order to achieve a high calculation
accuracy and a high run time efficiency. Optimisation of the radiation source has been
presented in Chapter 4. Optimisation of the geometry and the transport parameters in
electronic portal imaging device (EPID) simulation will be presented in this chapter.
Practically useful and scientifically interesting MC studies of EPIDs will be re-
ported. Beginning with dosimetrically verified amorphous silicon (a-Si) and scanning
liquid ionisation chamber (SLIC) EPID models, simplified models were designed by
first studying, layer-by-layer, the interaction types and energy depositions in the
EPIDs. The simplified models not only reduce MC simulation run times, but are also
potentially applicable to non-MC dose computation techniques. Effects of various
MC transport options on portal dose prediction in both EPIDs will also be reported.
88
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CHAPTER 6. OPTIMISATION OF MONTE CARLO SIMULATIONS 89
6.1 Introduction
In introducing the stages of radiation detection in EPIDs, Section 2.3 described the
converter and the detector as the two components forming “the heart” of the EPID
(Figure 2.6). For the a-Si EPID, the converter is a combination of a 1 mm copper
plate and a Gd2O2S:Tb screen; the detector is a glass substrate containing an array
of photodiodes. For the SLIC EPID, the converter is a 1 mm plastoferrite plate and
the detector is a layer of iso-octane, an organic liquid.
Various MC studies of megavoltage portal imaging have been reported. By MC
modelling the SLIC EPID, Keller et al. [1998] simulated dose spread kernels in units
of absolute dose per incident energy fluence. von Wittenau et al. [2002] investigated
dose components contributing to, and energy dependence of, image blurring on a
hypothetical a-Si imager. Using an algorithm by Radcliffe et al. [1993], both Kausch
et al. [1999] and Cremers et al. [2004], in their study of metal/phosphor imager
performance, included simulation of optical transport in the phosphor. Munro and
Mulligan [2002] investigated the effects of metal plate type and thickness on the
signal, subject contrast, signal contrast and detective quantum efficiency (DQE) of
EC-L portal film cassettes; a modified design was proposed. Ko et al. [2004] showed
that backscatter causes asymmetry in dosimetric images from an a-Si EPID; the
maximum thickness of backscatter material was theorised. Bissonnette et al. [1997,
2003] used the quantum accounting diagram (QAD) theory∗ and studied the optimal
phosphor thickness for portal imaging.
∗The QAD theory models a linear imaging system as a serial cascade of blur and gain stages.
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CHAPTER 6. OPTIMISATION OF MONTE CARLO SIMULATIONS 90
This work did not explore alternative constructions for manufacturing EPIDs,
but developed alternative models for computation of radiation quantities (e.g. dose)
in EPIDs. Formulation was therefore not subjected to the many constraints and
approximations in physical phantom fabrication [White et al. 1988]. Based on stud-
ies of radiation transport through complete detector models, simplified models were
designed and tested for the a-Si and the SLIC EPIDs respectively. The effects of
transport settings on MC simulation of both EPID types were also investigated. Ad-
ditionally, water-equivalence of both EPID types, which is pertinent in most non-MC
portal dosimetry techniques, was studied.
6.2 Materials and Methods
6.2.1 Radiation Transport Studies
This work began with dosimetrically working MC models of the a-Si [Siebers et al.
2004] and the SLIC [Spezi and Lewis 2002] EPIDs, which have been successfully
verified against measurements. The a-Si model contains 24 layers (Figure 6.1), while
the SLIC model contains 15 layers (Figure 6.4), of different materials according to
details provided by the manufacturer. In addition to the skeleton of a typical portal
imaging cassette given in Figure 2.6, both EPIDs contain internal support structures
and protective housing, where interleaving materials such as rohacell∗, FR4† and
∗The rohacell is a hard foam material.†The FR4 is a printed circuit board material.
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CHAPTER 6. OPTIMISATION OF MONTE CARLO SIMULATIONS 91
copper foils∗ can be commonly found.
To facilitate our understanding of radiation transport in the EPID, EGSnrc codes
were written to tally the interaction type, energy deposition and backscatter contri-
bution in each layer of the a-Si and the SLIC EPIDs respectively. The EPIDs were
irradiated by a 6 MV 10 cm × 10 cm beam, using a phase space file previously gen-
erated from a BEAMnrc simulation (Chapter 4). The relevance of this MC study
will become evident in Section 6.3.1, as interaction types and energy deposition in
each layer may not be directly intuitive (e.g. from lookup tables) since each layer
is of varying thickness and many are compounds of different elements in different
proportions.
6.2.2 Design of Simplified EPID Models
A fully detailed, multi-layered model entail frequent boundary crossing during MC
simulations (causing long run times) and cannot be readily implemented for non-MC
calculations (e.g. conventional TPSs, convolution/superposition techniques.) Sim-
plified models could therefore be useful as alternatives for dosimetric computation.
Aided by the results from Section 6.2.1, we designed simplified models for the a-Si
(detailed in Section 6.2.2.1) and the SLIC (detailed in Section 6.2.2.2) respectively.
Each simplified EPID model was tested against the respective complete model by
comparing portal dose profiles under 4 irradiation setups:
1. a 2 cm × 2 cm open field†;
∗The copper foils are cladding on the FR4 layers to isolate/ground electrically the materialssurrounding the EPID.
†An open field is a radiation field without any object placed in the beam.
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CHAPTER 6. OPTIMISATION OF MONTE CARLO SIMULATIONS 92
2. a 10 cm × 10 cm open field;
3. a 20 cm × 20 cm open field; and
4. a 20 cm × 20 cm open field, with a 20 cm-thick, 32.5 cm × 32.5 cm water
phantom positioned at SSD 114 cm, which resulted in the minimum phantom-
to-EPID air gap distance for a SDD of 140 cm.∗ The minimum air gap distance
was to provide high scatter as a stringent test condition. The centre of the water
phantom was aligned to the isocentre in longitudinal and lateral directions.
In each test, to reduce statistical noise, a portal dose profile was tallied over a 4
cm-wide band centred on the central axis – for all cases except when the beam was 2
cm × 2 cm, where a 1.6 cm-wide band was used instead. The number of histories per
hour and the standard error of the tallies were observed. Where a portal dose profile
is tallied, simulations in this work assumed 100% pixel fill factor† i.e. that the entire
area of each pixel is radiation sensitive.
Where a profile B is compared against a profile A, each profile was first normalised
to its value at the central axis. Dloc, the local point-to-point difference, and Dcax, the
difference with respect to the central axis value, were calculated:
Dloc =Ai −Bi
Ai+Bi
2
(6.1)
Dcax =Ai −Bi
Ao
(6.2)
∗SSD, SDD and the phantom-EPID air gap distance have been defined in Figure 2.6.†The fill factor is the percentage of radiation sensitive area, which is usually less than 100% due
to the electronics circuitry around each pixel.
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CHAPTER 6. OPTIMISATION OF MONTE CARLO SIMULATIONS 93
where subscript i denotes the ith point on the profile, and Ao denotes the value at
central axis of the reference profile A. The purpose of calculating both Dloc and Dcax
was to provide information for two criteria, decided upon according to the circum-
stances. The former is more conservative, e.g. at the field umbra in Figure 6.7a, Ai
and Bi are less than 5% of Ao. Therefore, Dcax would be lower than Dloc. At the
practical level, a high Dloc in the field umbra could be insignificant compared to the
dose prescribed to point Ao.
6.2.2.1 A Simplified a-Si EPID Model
Two simplified a-Si EPID models were tested and compared with the original model.
Models are labelled as follows:
A. the original, full 28-layered model as specified by the manufacturer;
B. a model simplified from model A, consisting of 11 layers, 3 of which were
vacuum; and
C. a model simplified from model A, consisting of 16 layers, 3 of which were
vacuum.
6.2.2.2 A Simplified SLIC EPID Model
A 4-layer simplified SLIC EPID model was designed. The 4 layers are:
1. the top cover of a medium composed of elements from the polystyrene, air,
rohacell and two FR4 layers of the original model. By specifying the summed
proportion-by-weight of each element, cross section data for the medium were
generated using pre-processor PEGS4 [Kawrakow and Rogers 2002]. To main-
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CHAPTER 6. OPTIMISATION OF MONTE CARLO SIMULATIONS 94
tain the beam divergence incident on the active detection layer∗, the thickness
of the top cover was set equal to the total thickness of the layers it replaced.
The density was calculated so that the total weight remained unchanged.
2. the buildup or photon-to-electron converter (plastoferrite) is kept but relocated
immediately upstream from the active detection layer.
3. the active detection layer is left unchanged.
4. the back cover is reduced to a 0.8 mm-thick FR4 layer.
All copper layers (each 1.6 µm-thick) were not included in the simplified SLIC EPID
model.
6.2.3 Selection of Transport Options
With the release of the nrc versions of EGS, BEAM and DOSXYZ, various transport
options became user-selectable. While there is a default setting which should be
adequate for most radiotherapy applications, it should not be taken for granted to
produce accurate results for all problems. We investigated the following transport
options in DOSXYZnrc simulations for the a-Si and the SLIC portal dose predictions
respectively:
1. bound Compton scattering ON or OFF (the default). ON is more accurate but
the difference is expected to be insignificant except at very low energies [Johns
and Cunningham 1983].
∗The active detection layer is the layer containing iso-octane.
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CHAPTER 6. OPTIMISATION OF MONTE CARLO SIMULATIONS 95
2. electron boundary crossing algorithm EXACT or PRESTA-I (the default). EX-
ACT is more accurate but the difference is usually negligible at high energies.
It switches into single elastic scattering mode near boundaries. PRESTA-I is
more efficient.
3. pair production angular sampling SIMPLE (the default) or Koch-Motz.
4. photoelectron angular sampling OFF (the default) or ON.
5. bremsstrahlung angular sampling SIMPLE (the default) or Koch-Motz.
6. atomic relaxation ON or OFF (the default). ON is more accurate although
simulations take longer.
7. spin effects ON (the default) or OFF. ON is more accurate although simulations
take longer.
8. global electron cutoffs 0.521 MeV or 0.7 MeV (rest mass included). When an
electron’s energy falls below this cutoff, its track its terminated with all its
remaining energy deposited locally. A higher cutoff is more efficient but may
bias simulation results.
Further details of the transport options are described in the literature [Kawrakow and
Rogers 2002, Kawrakow 2000a]. The full, original EPID models (not the simplified
models designed in Section 6.2.2) were used for this section. A 6 MV 15 cm × 15 cm
beam was directed from 45◦ gantry angle on a 20 cm perspex cube embedded with a
5 cm × 5 cm × 4 cm air gap at the centre. For each of the transport options listed
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CHAPTER 6. OPTIMISATION OF MONTE CARLO SIMULATIONS 96
above, simulations were run with the default and non-default selections in a paired
test. Portal dose profiles were compared.
6.2.4 Comparison with Other Techniques
Most non-MC portal dose predictions [Boellaard et al. 1996, McNutt et al. 1996, van
Esch et al. 2001, 2004, Vieira et al. 2004] 1) employ convolution/superposition calcu-
lation algorithms; and 2) calibrate image pixel values against ion chamber readings,
thereby intrinsically assume water-equivalence of the EPID in terms of dosimetric
properties. Effects of calculation algorithms on calculation outcome and the superior-
ity of MC over convolution/superposition techniques have been widely demonstrated
(see Ahnesjo and Aspradakis [1999] and references therein). This work investigated
the inaccuracies due to the assumption of EPID water-equivalence, by simulating a
water slab (with sufficient buildup and backscatter) of the same area and extracting
dose profiles at the depth of maximum dose under 4 irradiation conditions similar
to those in Section 6.2.2. These profiles were compared against profiles from the
complete a-Si and SLIC models.
6.3 Results & Discussion
Figure 6.1 shows the count for each interaction type in the a-Si model. Figure 6.2
shows the energy deposition in each layer, by particles which eventually contributed
to the signal, and those which did not. The copper converter layer situated 3 layers
above the screen recorded the highest event count: 20% out of the total. It recorded
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CHAPTER 6. OPTIMISATION OF MONTE CARLO SIMULATIONS 97
5 times as many Compton events as photoelectric events. Here, the bremsstrahlung
event count was the highest of all layers. The function of this copper converter
layer is distinct from the other, much thinner, copper foils. It is not only to convert
photons into electrons (which are to form image signal), but also to absorb low-
energy scattered particles (to reduce noise contribution to the signal). The former is
evident from Figure 6.2, where signal-contributing energy deposition was higher in
this copper layer than any of the layers above the screen. The latter is evident from
the same figure, where, among the layers above the screen, non-signal-contributing
energy deposition was only second to that of the top cover.
6.3.1 Radiation Transport Studies
6.3.1.1 The a-Si
Event count in the Gd2O2S:Tb (gadolinium oxysulphide terbium activated) screen
was 12% of the total. The ratio of photoelectric, Compton and pair production
event counts was 39:24:1. In real-life operation, the screen would convert electrons
(mostly generated from the copper buildup layer) into light, which would be detected
by the photodiodes in the glass substrate downstream to the screen; detection of
photodiode signals form the portal image. In MC simulations, however, interactions
are not explicitly simulated below 10 keV (explained in Section 3.1). Consequently,
the following processes are not simulated explicitly: conversion into light, transport of
optical photons from the scintillator to the photodiode, direct interactions of photons
and electrons with the photodiodes, and generation of photodiode signals. Instead,
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CHAPTER 6. OPTIMISATION OF MONTE CARLO SIMULATIONS 98
BR
EM
SS
TR
AH
LU
NG
AN
NIH
ILA
TIO
N
MO
LL
ER
& B
HA
BH
A
FL
UO
RE
SC
EN
CE
PA
IR P
RO
DU
CT
ION
PH
OT
OE
LE
CT
RIC
CO
MP
TO
N
cover
air
FR4
rohacell
coat
foamFR4
filter
paper
SCREEN
GLASS SUBSTRATE
polystyrene
1 mm COPPER
copper foil
nickel
FR4
copper foil
air
FR4rohacell
paper
converts electrons to light
converts photons to electrons
epoxy
aluminiumwater
Figure 6.1: Count of each interaction type in each layer of the a-Si EPID. Grayscale is inlog10. Thicknesses do not reflect true layer thicknesses.
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CHAPTER 6. OPTIMISATION OF MONTE CARLO SIMULATIONS 99
converts photons to electrons
air
cover
nickel
FR4rohacell
FR4
rohacell
FR4
paper
filter
coat
paper
polystyrene
foam
SCREEN
GLASS SUBSTRATE
FR4air
copper foil
1 mm COPPER
converts electrons to light
copper foil
epoxy
aluminium
water
signal−contributing particles non−signal−contributing particlesenergy deposited by energy deposited by
Figure 6.2: Energy deposition (MeV) in each layer of the a-Si EPID, by particles whichdeposited energy in the Gd2O2S:Tb layer, and those which did not. Grayscale is given inlog10. Thicknesses do not reflect true layer thicknesses.
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CHAPTER 6. OPTIMISATION OF MONTE CARLO SIMULATIONS 100
energy deposition in the screen is tallied to form the predicted portal image, as
commonly practised and has been found to successfully predict portal dose [Siebers
et al. 2004]. This may be explained by our understanding that direct interactions
of photons and electrons with the photodiodes make sub-percent contribution to the
total signal, and that photodiode response is proportional to the energy deposited in
the phosphor [Munro and Bouius 1998].
The screen contains gadolinium, which has an absorption edge at 50.2 keV, ex-
plaining the fluorescence (Figure 6.1). Fluorescence was not recorded in any other
layers because no other element in the a-Si model has an absorption edge above 10
keV, below which electron interactions were not simulated explicitly.
The glass layer below the screen recorded 15% of the total event count. This is
where, in an actual a-Si EPID, the glass substrate containing an array of photodiodes
resides. Photodiodes were not modelled in our simulations.
The nickel and aluminium layers, due to their micron-scale thickness, recorded
less than 0.1% of the total event count. The FR4 layers each contributed 4 to 6%
to the events count; whereas the rohacell layers each contributed 2 to 3%. Out of
all signal-contributing energy deposition (Figure 6.2), only 0.04% and 0.005% were
from the FR4 and rohacell layers respectively. Out of all non-signal-contributing
energy deposition, 0.9% and 0.2% were in the FR4 and rohacell layers respectively.
In Section 6.2.2, FR4 and rohacell layers are to be excluded from the simplified a-Si
models.
Figure 6.3 shows energy deposition by particles backscattered from layers below
the screen (left) and that by particles which were never backscattered from any of
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CHAPTER 6. OPTIMISATION OF MONTE CARLO SIMULATIONS 101
water
aluminium
epoxy
air
FR4
rohacell
FR4
paper
glass
filter
coat
copper foil
SCREEN
backscattered particlesenergy deposited by
all other particlesenergy deposited by
Figure 6.3: Energy deposition (MeV) in the a-Si EPID by particles backscattered fromlayers below the screen (left) and that by particles which were never backscattered fromany of the layers below the screen (right). Grayscale is given in log10. Thicknesses do notreflect true layer thicknesses.
the layers below the screen (right). 18% of the total energy deposited in the screen
was by backscattered particles.
6.3.1.2 The SLIC
Figure 6.4 shows the count for each interaction type in the SLIC model. Figure 6.5
shows the energy deposition in each layer, by particles which deposited energy in
the iso-octane layer, and those which did not. 40% of the events took place in the
plastoferrite layer, 10% in each FR4 layer and 1% in each copper layer (1.6 µm-thick).
It follows that these copper layers can be excluded from the simplified SLIC model
in Section 6.2.2 without affecting the results unduly.
The plastoferrite layer exhibited its distinctive role analogous to the copper buildup
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CHAPTER 6. OPTIMISATION OF MONTE CARLO SIMULATIONS 102
BR
EM
SS
TR
AH
LU
NG
AN
NIH
ILA
TIO
N
MO
LL
ER
& B
HA
BH
A
FL
UO
RE
SC
EN
CE
PA
IR P
RO
DU
CT
ION
PH
OT
OE
LE
CT
RIC
CO
MP
TO
N
FR4
rohacell
FR4
FR4
ISO−OCTANE
copper foil
copper foil
rohacell
copper foil
copper foil
copper foil
FR4
air
polystyrene
active detection layer
PLASTOFERRITEconverts photons to electrons
Figure 6.4: Count of each interaction type in each layer of the SLIC EPID. Grayscale isin log10. Thicknesses do not reflect true layer thicknesses.
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CHAPTER 6. OPTIMISATION OF MONTE CARLO SIMULATIONS 103
FR4
polystyrene
air
FR4
copper
rohacell
copper
FR4
copper
rohacell
copper
FR4
copper
PLASTOFERRITE
ISO−OCTANE
converts photons to electrons
active detection layer
signal−contributing particles non−signal−contributing particlesenergy deposited by energy deposited by
Figure 6.5: Energy deposition (MeV) in each layer of the SLIC EPID, by particles whichdeposited energy in the iso-octane layer (left), and those which did not deposit energy inthe iso-octane layer (right). Grayscale is given in log10. Thicknesses do not reflect truelayer thicknesses.
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CHAPTER 6. OPTIMISATION OF MONTE CARLO SIMULATIONS 104
layer in the a-Si EPID – it not only converts photons to electrons to produce ionisa-
tion for detection, but also stops low energy particles, as evident from the high energy
deposition by non-signal-contributing particles (Figure 6.5). The relative proportion
of Compton, photoelectric and pair production event count was 120:6:1. Plastofer-
rite contains strontium, which has an absorption edge at 16.1 keV. This explains the
fluorescence. Fluorescence was not recorded in any other layers because no other ele-
ment in the SLIC model has an absorption edge above 10 keV, below which electron
interactions were not simulated explicitly.
The iso-octane (2,2,4 trimethylpentane) layer is the active detection layer where
signal is read out for image formation. In this layer, 33% were Compton events,
while photoelectric events were 3 orders of magnitude lower. In real-life operation,
detection of ionising radiation depends not on free electrons but on heavy ion (e.g.
ionised trimethylpentane, ionised water or oxygen) transport – free electron trans-
port does not occur because free electrons quickly bind to water, oxygen or other
electronegative contaminants [van Herk 1991, Holroyd and Anderson 1985]. In our
MC simulations, however, heavy ion transport was not simulated. Instead, energy de-
position by charged particles in the iso-octane layer was tallied to form the predicted
portal image. This approximation has been found to be valid over a wide range of
source-phantom-detector setups [Chin et al. 2005].
Event counts, however, may not reflect the amount of energy absorbed. Although
the bottom-most 4 layers recorded considerable event counts (Figure 6.4), signal-
contributing energy depositions were minimal (Figure 6.5). It follows that in Sec-
tion 6.2.2, these 4 layers are to be excluded from the simplified model.
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CHAPTER 6. OPTIMISATION OF MONTE CARLO SIMULATIONS 105
Figure 6.6 shows energy deposition by particles backscattered from layers below
the iso-octane layer and that by particles which were never backscattered from any
of the layers below the iso-octane layer. 15% of the total energy deposited in the iso-
octane layer was by backscattered particles. Among all layers below the iso-octane
layer, signal-contributing backscattered particles deposited most energy (93%) in the
FR4 layer immediately below the iso-octane layer. It follows that in Section 6.2.2,
this FR4 layer is to represent the backscatter material – all other layers below it are
to be excluded from the simplified model.
rohacell
FR4
FR4
copper foil
copper foil
iso−octane
backscattered particlesenergy deposited by energy deposited by
all other particles
Figure 6.6: Energy deposition (MeV) in the SLIC EPID by particles backscattered fromlayers below the iso-octane layer (left) and that by particles which were never backscat-tered from any of the layers below the iso-octane layer (right). Grayscale is given in log10.Thicknesses do not reflect true layer thicknesses.
6.3.2 Design of Simplified EPID Models
Figure 6.7 compares portal dose profiles from a-Si models A and B. (In this work,
where profiles are symmetrical about their central axis, values at symmetrical points
have been averaged and plotted as a single point.) In the order of irradiation condi-
tions listed in Section 6.2.2, Dcax was within 1.0%, 1.0%, 1.5% and 1.5% respectively,
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CHAPTER 6. OPTIMISATION OF MONTE CARLO SIMULATIONS 106
while Dloc was within 19%, 29%, 14% and 5.2% respectively. Figure 6.8 compares
portal dose profiles from a-Si models A and C: Dcax was always within 1.0%, while
Dloc was within 12%, 23% 11% and 3.7% respectively.
Whether models B and C are valid approximations of model A is at the user’s
discretion according to the desired agreement. Simulations of models B and C reduced
the number of histories simulated per unit time by 46% and 36% respectively. For a
given number of histories, standard errors of the tallies were found to be independent
of the model used.
Figure 6.9 compares portal dose profiles from the simplified SLIC model against
that from the complete model. Except for outliers due to statistical noise, Dcax was
within 1% for all 4 irradiation configurations tested; whereas Dloc was 18%, 105%,
25% and 1.4% respectively. The simplified model halved the MC run time in open
field portal dose prediction.
Results of tests on the simplified a-Si and SLIC EPID models are summarised in
Figure 6.10, where the root-mean-square of the difference (from the respective full
models) with respect to the central axis value is plotted. Among the irradiation con-
ditions tested, simplified EPID models were found to be most accurate for irradiation
condition 1 (square field of 2 cm side); least accurate for irradiation condition 3 (20
cm square field with a water phantom in the beam).
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CHAPTER 6. OPTIMISATION OF MONTE CARLO SIMULATIONS 107
0 5 10 15position (cm)
0.0
0.2
0.4
0.6
0.8
1.0
dose (normalised)
0 5 10 15position (cm)
-2
-1
0
1
2
Dcax(%)
0 5 10 15position (cm)
-20
-10
0
10
20
Dloc(%)
0 5 10 15position (cm)
-2
-1
0
1
2
Dcax(%)
0 5 10 15position (cm)
-6
-4
-2
0
2
4
6
Dloc(%)
0 5 10 15position (cm)
0.0
0.2
0.4
0.6
0.8
1.0
dose (normalised)
0 1 2 3position (cm)
-1
0
1
Dcax(%)
0 1 2 3position (cm)
-20
-10
0
10
20
Dloc(%)
0 1 2 3position (cm)
0.0
0.2
0.4
0.6
0.8
1.0
dose (normalised)
0 5 10 15position (cm)
-1
0
1
Dcax(%)
0 5 10 15position (cm)
-40
-20
0
20
40
Dloc(%)
0 5 10 15position (cm)
0.0
0.2
0.4
0.6
0.8
1.0
dose (normalised)
c
ba
d
Figure 6.7: a-Si models A (black lines) versus B (red crosses): dose profiles and corre-sponding differences when each EPID model was irradiated by a a) 2 cm × 2 cm open field;b) 10 cm × 10 cm open field; c) 20 cm × 20 cm open field; and d) 20 cm × 20 cm field,water phantom in the field.
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CHAPTER 6. OPTIMISATION OF MONTE CARLO SIMULATIONS 108
0 1 2 3position (cm)
0.0
0.2
0.4
0.6
0.8
1.0
dose (normalised)
0 1 2 3position (cm)
-0.5
0
0.5
Dcax(%)
0 1 2 3position (cm)
-10
0
10
Dloc(%)
0 5 10 15position (cm)
0.0
0.2
0.4
0.6
0.8
1.0
dose (normalised)
0 5 10 15position (cm)
-1
0
1
Dcax(%)
0 5 10 15position (cm)
-40
-20
0
20
40
Dloc(%)
0 5 10 15position (cm)
0.0
0.2
0.4
0.6
0.8
1.0
dose (normalised)
0 5 10 15position (cm)
-2
-1
0
1
2
Dcax(%)
0 5 10 15position (cm)
-10
0
10
Dloc(%)
0 5 10 15position (cm)
0.0
0.2
0.4
0.6
0.8
1.0
dose (normalised)
0 5 10 15position (cm)
-1
0
1
Dcax(%)
0 5 10 15position (cm)
-4
-2
0
2
4
Dloc(%)
c
ba
d
Figure 6.8: a-Si models A (black lines) versus C (red crosses): dose profiles and corre-sponding differences when each EPID model was irradiated by a a) 2 cm × 2 cm open field;b) 10 cm × 10 cm open field; c) 20 cm × 20 cm open field; and d) 20 cm × 20 cm field,water phantom in the field.
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CHAPTER 6. OPTIMISATION OF MONTE CARLO SIMULATIONS 109
0 1 2 3position (cm)
0.0
0.2
0.4
0.6
0.8
1.0
dose (normalised)
0 1 2 3position (cm)
-1
0
1
Dcax(%)
0 1 2 3position (cm)
-20
-10
0
10
20
Dloc(%)
0 5 10 15position (cm)
0.0
0.2
0.4
0.6
0.8
1.0
dose (normalised)
0 5 10 15position (cm)
-3
-2
-1
0
1
2
3
Dcax(%)
0 5 10 15position (cm)
-200
-100
0
100
200
Dloc(%)
0 5 10 15position (cm)
0.0
0.2
0.4
0.6
0.8
1.0
dose (normalised)
0 5 10 15position (cm)
-4
-2
0
2
4
Dcax(%)
0 5 10 15position (cm)
-40
-20
0
20
40
Dloc(%)
0 5 10 15position (cm)
0.0
0.2
0.4
0.6
0.8
1.0
dose (normalised)
0 5 10 15position (cm)
-1
0
1
Dcax(%)
0 5 10 15position (cm)
-10
0
10
Dloc(%)
c
ba
d
Figure 6.9: The full SLIC model (black lines) versus the simplified SLIC model (redcrosses): dose profiles and corresponding differences when each EPID model was irradiatedby a a) 2 cm × 2 cm open field; b) 10 cm × 10 cm open field; c) 20 cm × 20 cm open field;and d) 20 cm × 20 cm field, water phantom in the field.
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CHAPTER 6. OPTIMISATION OF MONTE CARLO SIMULATIONS 110
1 2 3 40
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
IRRADIATION CONDITION
RM
S
a−Si substitute model B
a−Si substitute model C
SLIC substitute
���������������������
���������������������
RM
S D
IFF
ER
EN
CE
(%
)
Figure 6.10: The simplified a-Si EPID models (B and C) and the simplified SLIC EPIDmodel compared to the full a-Si and SLIC models respectively: root-mean-square of thedifferences under irradiation conditions 1 (2 cm-side square field), 2 (10 cm-side squarefield), 3 (20 cm-side square field) and 4 (20 cm-side square field with a water phantom inthe beam).
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CHAPTER 6. OPTIMISATION OF MONTE CARLO SIMULATIONS 111
0 5 10 15 20position (cm)
-1
0
1
Dcax(%)
0 5 10 15 20position (cm)
-20
-10
0
10
20Dloc(%)
0 5 10 15 20position (cm)
-1
0
1
Dcax(%)
0 5 10 15 20position (cm)
-20
-10
0
10
20
Dloc(%)
0 5 10 15 20position (cm)
-1
0
1
Dcax(%)
0 5 10 15 20position (cm)
-20
-10
0
10
20
Dloc(%)
0 5 10 15 20position (cm)
-1
0
1
Dcax(%)
0 5 10 15 20position (cm)
-20
-10
0
10
20
Dloc(%)
0 5 10 15 20position (cm)
-1
0
1
Dcax(%)
0 5 10 15 20position (cm)
-20
-10
0
10
20
Dloc(%)
0 5 10 15 20position (cm)
-1
0
1
Dcax(%)
0 5 10 15 20position (cm)
-20
-10
0
10
20
Dloc(%)
0 5 10 15 20position (cm)
-1
0
1
Dcax(%)
0 5 10 15 20position (cm)
-20
-10
0
10
20
Dloc(%)
0 5 10 15 20position (cm)
-1
0
1
Dcax(%)
0 5 10 15 20position (cm)
-20
-10
0
10
20
Dloc(%)
c
a b
d
fe
g h
Figure 6.11: Effects of transport options on the SLIC EPID calculated as Dloc (blue circles)and Dcax (black crosses): a) bound Compton scattering; b) electron boundary crossing; c)pair production angular sampling; d) photoelectron angular sampling; e) bremsstrahlungangular sampling; f) atomic relaxation; g) spin effects and h) global electron cutoff.
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CHAPTER 6. OPTIMISATION OF MONTE CARLO SIMULATIONS 112
0 5 10 15 20position (cm)
-3
-2
-1
0
1
2
3
Dcax(%)
0 5 10 15 20position (cm)
-6
-4
-2
0
2
4
6Dloc(%)
0 5 10 15 20position (cm)
-3
-2
-1
0
1
2
3
Dcax(%)
0 5 10 15 20position (cm)
-6
-4
-2
0
2
4
6
Dloc(%)
0 5 10 15 20position (cm)
-3
-2
-1
0
1
2
3
Dcax(%)
0 5 10 15 20position (cm)
-6
-4
-2
0
2
4
6
Dloc(%)
0 5 10 15 20position (cm)
-3
-2
-1
0
1
2
3
Dcax(%)
0 5 10 15 20position (cm)
-6
-4
-2
0
2
4
6
Dloc(%)
0 5 10 15 20position (cm)
-3
-2
-1
0
1
2
3
Dcax(%)
0 5 10 15 20position (cm)
-6
-4
-2
0
2
4
6
Dloc(%)
0 5 10 15 20position (cm)
-3
-2
-1
0
1
2
3
Dcax(%)
0 5 10 15 20position (cm)
-6
-4
-2
0
2
4
6
Dloc(%)
0 5 10 15 20position (cm)
-3
-2
-1
0
1
2
3
Dcax(%)
0 5 10 15 20position (cm)
-6
-4
-2
0
2
4
6
Dloc(%)
0 5 10 15 20position (cm)
-3
-2
-1
0
1
2
3
Dcax(%)
0 5 10 15 20position (cm)
-6
-4
-2
0
2
4
6
Dloc(%)
c
a b
d
fe
g h
Figure 6.12: Effects of transport options on the a-Si EPID calculated as Dloc (blue circles)and Dcax (black crosses): a) bound Compton scattering; b) electron boundary crossing; c)pair production angular sampling; d) photoelectron angular sampling; e) bremsstrahlungangular sampling; f) atomic relaxation; g) spin effects and h) global electron cutoff.
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CHAPTER 6. OPTIMISATION OF MONTE CARLO SIMULATIONS 113
6.3.3 Selection of Transport Options
For the transport options tested, no statistically significant difference was discernible
for the SLIC model (Figure 6.11). Overall, Dcax was within 1%. The a-Si model,
however, demonstrated obvious bias (Figure 6.12) when 1) atomic relaxation was
turned on: Dloc up to 4%, portal dose was over-estimated; 2) spin effects were turned
off Dloc: over 1.5%, portal dose was under-estimated; and 3) global electron cutoff was
set to 0.7 MeV (rest mass included): Dloc up to 5%, portal dose was over-estimated.
Dcax nonetheless remained consistently within 3% in all cases. For simulations of
the a-Si EPID, it is therefore recommended that atomic relaxation be turned on
(DOSXYZnrc turns this off by default) and that caution be taken when exercising
electron cutoffs. Interestingly, Munro and Mulligan [2002] reported no reduction in
calculation accuracy when both AE (below which secondary charged particles are
not explicitly simulated) and ECUT were set to 0.7 MeV (rest mass included) in
simulation of the EC-L cassette. Conditions under which this test was done were,
however, not reported.
For both a-Si and SLIC EPIDs, no statistically significant difference was found
whether or not Koch-Motz angular sampling was switched ON. This is understood
to be partly due to the insignificant contribution of bremsstrahlung events to energy
deposition in the EPIDs. In theory, Koch-Motz angular sampling is understood to
be more accurate at energies above radiotherapy range; however, since it is derived
from extreme relativistic approximations, its relevance at the radiotherapy range of
energies is unclear [Kawrakow and Rogers 2002].
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CHAPTER 6. OPTIMISATION OF MONTE CARLO SIMULATIONS 114
6.3.4 Comparison with Other Techniques
Figure 6.13 compares dose profiles from the a-Si EPID and those from a water-slab
EPID. Dcax up to 10% were found. For square fields of side 20 cm, the water-slab
EPID 1) underestimated off-axis portal dose for open fields; 2) overestimated off-
axis portal dose in the field, but underestimated portal dose in the umbra, when a
water phantom was place in the beam. No improvement was found even when an
extra buildup layer was added to the cassette cover of the complete a-Si model. Our
MC investigation confirms results from ion chamber measurements that the a-Si is
not water-equivalent [El-Mohri et al. 1999]. Discrepancies were found to be worse
at large field sizes (Figure 6.13) – which might explain the ‘field size dependency’
reported in work assuming water equivalence of the EPID [Grein et al. 2002, Greer
and Popescu 2003].
Figure 6.14 compares dose profiles from a SLIC EPID and those from a water-slab
EPID. Dloc was high (in some cases exceeding 80%) except for irradiation condition
4, where a water phantom was placed in the beam. Departure of the SLIC EPID
from water-equivalence has also been suggested from measurements by Essers et al.
[1996] and Chang et al. [2001]. Keller et al. [1998] found large absolute differences
when comparing dose spread kernels (integrated over the entire portal dose plane)
calculated for the SLIC EPID and for water. However, Figure 6.14 also shows that
Dcax was within 3%. Depending on the tolerance, it is thus the choice of the informed
user whether the representation of the SLIC EPID by a water slab is acceptable.
Results of tests on water-slab EPID models are summarised in Figure 6.15, where
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CHAPTER 6. OPTIMISATION OF MONTE CARLO SIMULATIONS 115
0 1 2 3position (cm)
-4
-2
0
2
4
Dcax(%)
0 1 2 3position (cm)
-60
-40
-20
0
20
40
60
Dloc(%)
0 1 2 3position (cm)
0.0
0.2
0.4
0.6
0.8
1.0
dose (normalised)
0 5 10 15position (cm)
0.0
0.2
0.4
0.6
0.8
1.0
dose (normalised)
0 5 10 15position (cm)
-4
-2
0
2
4
Dcax(%)
0 5 10 15position (cm)
-80
-40
0
40
80
Dloc(%)
0 5 10 15position (cm)
0.0
0.2
0.4
0.6
0.8
1.0
dose (normalised)
0 5 10 15position (cm)
-8
-6
-4
-2
0
2
4
6
8
Dcax(%)
0 5 10 15position (cm)
-60
-40
-20
0
20
40
60
Dloc(%)
0 5 10 15position (cm)
0.0
0.2
0.4
0.6
0.8
1.0
dose (normalised)
0 5 10 15position (cm)
-10
-5
0
5
10
Dcax(%)
0 5 10 15position (cm)
-40
-20
0
20
40
Dloc(%)
c
ba
d
Figure 6.13: a-Si EPID (black lines) versus water-slab EPID (red crosses): dose profilesand corresponding differences when the EPID was irradiated by a a) 2 cm × 2 cm openfield; b) 10 cm × 10 cm open field; c) 20 cm × 20 cm open field; and d) 20 cm × 20 cmfield, water phantom in the field.
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CHAPTER 6. OPTIMISATION OF MONTE CARLO SIMULATIONS 116
0 1 2 3position (cm)
0.0
0.2
0.4
0.6
0.8
1.0
dose (normalised)
0 1 2 3position (cm)
-3
-2
-1
0
1
2
3
Dcax(%)
0 1 2 3position (cm)
-40
-20
0
20
40
Dloc(%)
0 5 10 15position (cm)
0.0
0.2
0.4
0.6
0.8
1.0
dose (normalised)
0 5 10 15position (cm)
-2
-1
0
1
2
Dcax(%)
0 5 10 15position (cm)
-100
-50
0
50
100
Dloc(%)
0 5 10 15position (cm)
0.0
0.2
0.4
0.6
0.8
1.0
dose (normalised)
0 5 10 15position (cm)
-2
-1
0
1
2
Dcax(%)
0 5 10 15position (cm)
-30
-20
-10
0
10
20
30
Dloc(%)
0 5 10 15position (cm)
0.0
0.2
0.4
0.6
0.8
1.0
dose (normalised)
0 5 10 15position (cm)
-1
0
1
Dcax(%)
0 5 10 15position (cm)
-4
-2
0
2
4
Dloc(%)
c
ba
d
Figure 6.14: SLIC EPID (black lines) versus water-slab EPID (red crosses): dose profilesand corresponding differences when each EPID model was irradiated by a a) 2 cm × 2 cmopen field; b) 10 cm × 10 cm open field; c) 20 cm × 20 cm open field; and d) 20 cm × 20cm field, water phantom in the field.
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CHAPTER 6. OPTIMISATION OF MONTE CARLO SIMULATIONS 117
1 2 3 40
0.5
1
1.5
2
2.5
3
3.5
4
IRRADIATION CONDITION
RM
S
a−Si
SLIC
������������������
������������������
RM
S D
IFF
ER
EN
CE
(%
)
Figure 6.15: Water-slab EPID models compared to the full a-Si and SLIC models respec-tively: root-mean-square of the differences under irradiation conditions 1 (2 cm-side squarefield), 2 (10 cm-side square field), 3 (20 cm-side square field) and 4 (20 cm-side square fieldwith a water phantom in the beam).
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CHAPTER 6. OPTIMISATION OF MONTE CARLO SIMULATIONS 118
the root-mean-square of the difference (from the full models) with respect to the
central axis value is plotted. Compared to the SLIC EPID, radiation properties of
the a-Si EPID are less water-equivalent – as expected due to the presence of phosphor,
a high-atomic-number material. For the SLIC and a-Si EPIDs, the highest-Z element
present are strontium (Z = 38, in plastoferrite) and gadolinium (Z = 64, in phosphor
screen) respectively.
6.4 Conclusions
For each of the a-Si and the SLIC EPIDs, simplified EPID models for dosimetric
computation have been designed and tested. For the a-Si EPID, Dcax was consistently
within 1.5% and 1.0% for simplified models B and C respectively. For the simplified
SLIC model, Dcax was generally within 1.5%. The simpler models not only reduce MC
simulation run time, but may be adopted as a more realistic model (e.g. compared
to a homogeneous water slab) for non-MC computations.
The effects of transport settings on portal image prediction have been investigated
for both the a-Si and the SLIC EPIDs. Whereas the SLIC EPID was found to be
insensitive to such effects under the irradiation conditions tested, the a-Si EPID
showed 4%, 1.5% and 5% of Dloc respectively when simulation of atomic relaxation
was turned on, when simulation of spin effects was turned off, and when electron cutoff
energy was set to 0.7 MeV (rest mass included). It should be noted that DOSXYZnrc
turns off atomic relaxation by default.
The assumption of water-equivalence of EPIDs, characteristic of many non-MC
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CHAPTER 6. OPTIMISATION OF MONTE CARLO SIMULATIONS 119
portal dosimetry techniques, was found to produce Dcax up to 10% and 3% for the
a-Si and SLIC EPIDs respectively. Our findings underscore the role of, and the need
for, MC radiation transport in radiotherapy portal dosimetric calculation.
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Chapter 7
PRACTICAL ASPECTS OF
PORTAL IMAGE ACQUISITION
The treatment verification solution presented in Chapter 5 works by comparing dose
maps obtained from Monte Carlo (MC) simulations with dose maps derived from
physically acquired portal images. Chapter 4 has already reported the optimisation
of the former. This chapter focuses on the optimisation of the latter.
Accurate derivation of dose information from image pixel values relies on the de-
tector (e.g. dose response and discharge characteristics) as well as the acquisition
system (e.g. readout and sequencing with respect to the beam.) Problems, solutions
and alternatives in the practical aspects of portal image acquisition for IMRT dose
verification will be reported. An alternative imaging sequence which overcomes the
problems identified will be proposed. A new way of interpreting portal images, in-
corporating both spatial and temporal information, will also be proposed. The idea
takes advantage of features commonly seen as limitations: ghosting∗ (often seen as
unwanted signals), and row-by-row image scanning (often seen as a delay).
∗Ghosting will be explained in Section 7.2.4.2.
120
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CHAPTER 7. PRACTICAL ASPECTS OF IMAGE ACQUISITION 121
7.1 Introduction
As mentioned in Chapter 5, the response of scanning liquid ionisation chamber (SLIC)
electronic portal imaging devices (EPIDs) varies with gantry angle, causing an arte-
fact commonly known as the bulging effect. A comprehensive study of this effect will
be presented, along with a rigorously tested correction algorithm developed by the
author.
This chapter also investigates the prospects of the Varian aS500 amorphous silicon
(a-Si) EPID as a dosemeter. Some unexpected problems suggest that the use of
this device for IMRT dose verification should await further developments from the
manufacturer (Section 7.2.2 and Section 7.2.3).
By proposing an alternative imaging sequence which overcomes the present limi-
tations, Section 7.2.4 attempts to address the clinical need for verifying IMRT beams.
Section 7.3.4.2 suggests that since it is hard to avoid ghosting in portal images, we
might as well make use of it, by incorporating both spatial and temporal information
in image interpretation. Illustrative examples will be given.
7.2 Materials & Methods
We used a Varian PortalVision Mk2 SLIC EPID installed locally at Velindre Cancer
Centre. It produces portal images of 256×256 pixels, where each square pixel has
dimension 1.27 mm, giving a 32.5 cm × 32.5 cm imaging area.
Since an a-Si EPID was not available at Velindre Cancer Centre during the ma-
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CHAPTER 7. PRACTICAL ASPECTS OF IMAGE ACQUISITION 122
jority of this project,∗ experiments on the a-Si EPID were carried out on the Varian
PortalVision aS500 model at two of our collaborating institutions: Virginia Com-
monwealth University (USA) and the Institute of Cancer Research / Royal Marsden
Hospital (UK). The aS500 produces portal images of 512×384 pixels. Each square
pixel has dimension 0.78 mm, giving a 40.0 cm × 30.0 cm imaging area.
7.2.1 The SLIC: Variation with Gantry Angles
The gantry of a linear accelerator (linac) is rotated when various beam delivery angles
are required. As the linac head rotates around the isocentre, so does the diametri-
cally opposed EPID. When attenuation and scatter conditions are unchanged, fluence
incident on the EPID and therefore the EPID’s response should ideally be invariant
with gantry angle. In practice, however, images taken at various gantry angles are
not identical due to several gantry-dependent factors as detailed below:
1. Change in radiation output exiting the linac head. This contributes
little effect. Whereas the recommended tolerance is 2% [Mayles et al. 1999],
local quality control experience indicates that linac output changes by no more
than 1% with gantry angle [Gray 2003].
2. Imperfect mechanical rigidity of the support arm. This may cause ver-
tical, longitudinal and lateral shifts of the imager with respect to the isocentre.
The inverse square relation indicates that at SDD† 140 cm, a 1.2 cm decrease in
vertical position may cause a 1.7% increase in fluence incident on the detector.
∗Three a-Si EPIDs were installed and commissioned at Velindre Cancer Centre in March 2005.†The SDD has been defined in Figure 2.6.
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CHAPTER 7. PRACTICAL ASPECTS OF IMAGE ACQUISITION 123
3. Change in response of the EPID. This factor, known colloquially as the
bulging effect, is the dominant factor. Change in detector response due to
cassette orientation is a known behaviour of the SLIC EPID [van Herk and
Meertens 1988, Roback and Gerbi 1995]. The image detector unit contains an
ionisation chamber filled with iso-octane∗. Since the cassette which contains
the liquid is not entirely rigid, the two plates of the ionisation chamber flex
as the gantry rotates, causing non-uniform thickness of the liquid film. This
artefact, visible as alternately dark and bright oval areas on open field† images
(Figure 7.1), introduces asymmetry to an otherwise flat radiation profile.
4. Scatter from surrounding structures such as floor, walls and ceiling.
At gantry angles of 0◦ and 180◦, the separation between the imager and the
floor/ceiling can be very small, potentially allowing backscattered radiation to
reach the detector. The extent of the effect also depends on the construction
materials used.
The latter three factors will be considered in this work.
Image acquisition was carried out in multiple sessions at 2-week intervals. The
dataset of images from each session was labelled as follows:
- Dataset 410: images acquired at every 10◦ gantry angle. Image calibration was
updated at the start of the session.
- Dataset 430: images acquired at every 30◦ gantry angle. Image calibration was
∗The iso-octane has been introduced in Section 2.3.†The open field has been defined in Section 6.2.2.
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CHAPTER 7. PRACTICAL ASPECTS OF IMAGE ACQUISITION 124
BEFORE AFTER
G360G350G340G330G320G310
G250 G260 G270 G280 G290 G300
G240G230G220G210G200G190
G130 G140 G150 G160 G170 G180
G120G110G100G90G80G70
G10 G20 G30 G40 G50 G60 G10 G20 G30 G40 G50 G60
G120G110G100G90G80G70
G130 G140 G150 G160 G170 G180
G240G230G220G210G200G190
G250 G260 G270 G280 G290 G300
G360G350G340G330G320G310
Figure 7.1: Images, acquired at various gantry angles, before and after correction using thetechnique devised in Section 7.2.1.4. Corresponding gantry angles are labelled. A commongrayscale window has been used for all images.
updated at the start of the session.
- Dataset 490: images acquired at gantry angles of 0◦, 90◦, 180◦ and 270◦. Image
calibration specific to each gantry angle was obtained by updating the calibra-
tion each time the gantry was rotated.
For all datasets, the EPID, irradiated by a 6 MV 25 cm × 25 cm open field, was
positioned at SDD 140 cm. To protect radiation-sensitive electronics on the imager,
this was deemed the maximum field size at SDD 140 cm. The centre of the imaging
area was aligned to the isocentre in longitudinal and lateral directions. Dose-rate was
allowed to stabilise before acquisition began. Dataset410 was used to describe gantry
dependence of images and to derive a new correction function, whose applicability
was demonstrated using dataset 430. Dataset 490 was used to investigate image
calibration specific to cardinal gantry angle.
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CHAPTER 7. PRACTICAL ASPECTS OF IMAGE ACQUISITION 125
0 5 10 15 20 25 30 35y (cm)
0.995
1.000
1.005
1.010
grayscale (normalised)
0 5 10 15 20 25 30 35x (cm)
0.98
1.00
1.02
1.04
grayscale (normalised)
0 50 100 150 200 250 300 350gantry angle (degrees)
0.98
1.00
1.02
1.04
1.06
grayscale (normalised)
c)
a)
x
y
b)
d)
Figure 7.2: a) A portal image with x and y axes defined; b) pixel values along the centralx axis; c) pixel values along the central y axis; d) pixel values of a fixed point at variousgantry angles. Pixel values have been normalised to C0.
Each image of 256 x 256 pixels will be denoted Iγ where γ is the gantry angle at
which the image was acquired. Value on each pixel is denoted Pγ,x,y, and the pixel
value averaged over 10×10 pixels around the central axis (CAX) is denoted Cγ. C0
is the Cγ value when γ is zero. x and y are the coordinates of the pixel in the LR and
GT directions∗ as defined in Figure 7.2a.
7.2.1.1 Angular Dependence of Images
Iγ from the datasets were analysed for:
1. variation of central axis pixel value (Cγ) with gantry angle.
∗LR for “Left-Right”, also known as crossplane. GT for “Gun-Target”, also known as inplane.
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CHAPTER 7. PRACTICAL ASPECTS OF IMAGE ACQUISITION 126
2. 2D variation of images (Iγ) with gantry angle.
3. reproducibility of I0 after gantry rotation(s).
4. settling of the liquid once the SLIC cassette was moved into a vertical orien-
tation, by comparing I90 taken successively (immediately, after 12
minute and
after another 12
minute) once the gantry had been rotated into position 90◦. A
similar exercise was repeated for gantry angle 270◦.
5. effects from gantry rotation, by comparing three I90 images acquired at repeated
rotations back and forth between gantry angles 90◦ and 270◦. Similarly, three
images at gantry angle of 270◦ acquired after repeated rotations were compared.
Where images were compared, each local pixel value from the first image (A)
and its counterpart from the second image (B) were used for element-by-element
calculation of the expression
D =A−B
12(A + B)
(7.1)
7.2.1.2 Backscatter from Surroundings
To check effects due to backscatter from surrounding structures, a MC model was
built, using manufacturer-specified and directly measured data, to represent the
turntable on the floor of a linac installation. The SLIC EPID was modelled as previ-
ously reported [Spezi and Lewis 2002]. Irradiation of a 6 MV 25 cm × 25 cm beam
was simulated with DOSXYZnrc using default transport parameters. This was fol-
lowed by another simulation without the floor structures. Doses deposited on the
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CHAPTER 7. PRACTICAL ASPECTS OF IMAGE ACQUISITION 127
active detection layer∗ from the two simulations were compared.
7.2.1.3 Reproducibility
Reproducibility of the EPID signal over time was monitored in two ways:
1. reproducibility of I0, by inter-comparison from four different sessions at approx-
imately monthly intervals.
2. reproducibility of images acquired at every 30◦ gantry angle. Images from 410
and 430 were compared. Each image was normalised to C0 of the respective
dataset.
Monitoring of reproducibility was to ensure that the same angular correction can
be applied over different sessions. It was not of interest to find out how long a
calibration could last before significant deviation. This has already been thoroughly
studied elsewhere [Essers et al. 1996, Louwe et al. 2004]. For accurate dosimetry (as
demonstrated in Section 5.3.1.1), it is our practice to perform image calibration at
the start of each session.
7.2.1.4 Angular Correction Function
If left uncorrected, image dependence on gantry angle can potentially lead to signif-
icant errors in dosimetric verification. Our aim was to correct not only for variation
along the x direction [Evans et al. 1999], but also variation along the y direction (not
accounted for in previous work). x and y are as defined in Section 5.2 and Figure 7.2a.
∗The active detection layer is the layer containing iso-octane.
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CHAPTER 7. PRACTICAL ASPECTS OF IMAGE ACQUISITION 128
Images from the datasets indicated that a simple sinusoidal trend could not fully
characterise the angular variation. A model providing a better fit to the data was
found to be:
Q(x, y, γ) = I sin(Ax+B) sin(Cy +D) sin(Eγ) + J sin(Fγ +H) + K (7.2)
where γ is the gantry angle at which the image was acquired, A, B, C, D, E, F, H,
J and K are coefficients to be derived empirically. Whereas the first term on the
right-hand side of Equation (7.2) describes the pixel-by-pixel variation with gantry
angle, the second accounts for sag due to non-rigidity of the support arm. The third
is an offset term.
Based on Iγ of dataset 410, images were downsampled from 256×256 pixels to
64×64 pixels. The downsampled images formed a dataset of 4 variables: x, y, γ and
Pγ,x,y. This dataset served as input for nonlinear regression. Three independent vari-
ables∗ were assigned: x, y and γ. The aim of the correction function was to return C0,
which is typically used for central-axis grayscale-to-dose calibration in portal dosime-
try [Spezi and Lewis 2002]. Therefore, the dependent variable† for the regression was
assigned the ratio of C0 to Pγ,x,y. By applying the modified Levenberg-Marquardt
algorithm proposed by More [1977], the SPSS‡ nonlinear regression module was used
to produce least square estimates of the coefficients. Regression produced coefficients
required by the function Q(x, y, γ). An image requiring correction would have its
grayscale values multiplied by the corresponding value from Q(x, y, γ), producing the
∗Independent variables are sometimes known as the explanatory variables.†Dependent variables are sometimes known as the outcome variables.‡Statistical analysis software. The website is at www.spss.com.
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CHAPTER 7. PRACTICAL ASPECTS OF IMAGE ACQUISITION 129
corrected image.
7.2.1.5 Comparison with Existing Techniques
Correction using the sinusoidal modulation technique devised herein (Equation (7.2))
was compared with two existing techniques:
1. gantry-dependent flood field∗ (FF) correction [van Esch et al. 2001], where the
FF in the standard calibration protocol is replaced by one which is gantry-
dependent:
FF (γ) =FF0 + FF90 + FF180 + FF270
4+ sin(γ)
FF90 − FF270
2(7.3)
where γ is the gantry angle and the subscripts indicate the gantry angle at
which the FF was acquired. FF(γ), derived from dataset 490, replaces FF in
the standard image calibration such that
J =Jo −DF
FF (γ)k (7.4)
where Jo and J are the images before and after calibration, k is the scalar mean
of all values in FF(γ). Division is element-by-element.
2. correction based on profile averaging [Evans et al. 1999]. For each image in
dataset 410, x-profiles were averaged to obtain an x-profile representative of the
respective gantry angle. The ratio of the representative x-profile for Iγ to that
of I0 is applied as the correction factor.
∗The flood field has been defined in Section 5.2.1.1.
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CHAPTER 7. PRACTICAL ASPECTS OF IMAGE ACQUISITION 130
In the text that follows, the gantry-dependent FF, profile averaging and sinusoidal
modulation techniques will be referred to as the first, second and third techniques
respectively.
Each technique was used to correct images from dataset 430, which was not used
to derive any of the correction coefficients. The intent was to test the techniques
on images of a different session, since a technique that does not require frequent
regeneration of correction coefficients was desired.
Correction coefficients of the latter two techniques were derived using images at
every 10◦. Additionally, to investigate the sensitivity of correction coefficients to
angular resolution, coefficients were also generated using images at every 30◦.
7.2.1.6 Application of the New Technique
Next, the sinusoidal correction technique was used to correct images of a 10 cm ×
10 cm open field as an alternative to the 25 cm × 25 cm field described earlier, at
various gantry angles. A scaling factor was applied to account for the change in
output factor due to field size. This would not be required in MC portal dosimetry
where the change in output would have been intrinsically accounted for (Chapter 5).
Images before and after correction were analysed for symmetry along the x-
direction. The region of interest was defined as 80% of the beam size. Profiles
were averaged over 10 pixels in the y direction. Difference of each pixel value Px from
its counterpart P−x on the opposite side of the CAX was calculated as
d =Px − P−x
12(Px + P−x)
(7.5)
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CHAPTER 7. PRACTICAL ASPECTS OF IMAGE ACQUISITION 131
7.2.2 The a-Si: an Artefact in the IMRT Acquisition Mode
�����������������������������������
�����������������������������������
������������������������������
������������������������������
DATA PULSE
IMRT MODE
DATA PULSE
STANDARD MODE
BEAM
time
Figure 7.3: The standard and the IMRT image acquisition modes: timing of data pulseswith respect to the beam. Shaded pulse is the refresh cycle.
Figure 7.3 shows the two imaging modes available in the PortalVision aS500 sys-
tem: the standard and the IMRT modes. For both modes, a few frames are read
out before the start of irradiation to eliminate any dark current or residual data.
This process is sometimes called refresh cycle, reset, forced discharge or blanking. In
the standard mode, no readout occurs during beam-on. Readout occurs only after
irradiation. By not capturing image frames between/during linac pulses, this mode
avoids linac pulsing artefacts. It is, however, not suitable for imaging over the entire
duration of a beam because the frame buffer would saturate. Imaging over the entire
duration of a beam attempts to use the EPID as an integrating dosemeter – which
is commonly accepted by the EPID community as the way to verify IMRT beams.
(The author proposes an alternative method in Section 7.2.4.1.)
To overcome the problem due to frame buffer saturation, the manufacturer intro-
duced the IMRT mode. By allowing periodic transfer of data from the frame buffer to
another storage, readout can occur continuously during irradiation without saturat-
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CHAPTER 7. PRACTICAL ASPECTS OF IMAGE ACQUISITION 132
ing the buffer. To minimise pulsing artefacts, multiple frames are averaged to form
a final image. A point to note is that on the current Varian PortalVision system,
individual frames cannot be recovered.
As a first step in testing the usability of the aS500 EPID as an integrating doseme-
ter, open field images for varying exposure duration were acquired using the IMRT
mode. Prior to that, DF/FF calibration∗ had been updated at the same SDD without
any extra buildup.
7.2.3 The a-Si: Variation with Gantry Angles
Whereas SLIC EPIDs are known to produce gantry-dependent artefacts (Section 7.2.1),
a-Si EPIDs are generally believed to be gantry-invariant. Putting aside such presump-
tions, this section subjected the aS500 EPID to tests similar to those done for the
SLIC EPID (Section 7.2.1). Open field images were acquired at various gantry angles.
These images were later examined for any systematic difference.
7.2.4 Ideas for IMRT Verification
7.2.4.1 An Alternative Imaging Sequence
Of the two modes available in the Varian PortalVision acquisition system (Sec-
tion 7.2.2), neither is suitable for verifying IMRT beams. Whereas the standard mode
saturates before the beam finishes, the IMRT mode leads to the artefacts described
in Section 7.3.2. Additionally, assuming and using the EPID as an integrating or cu-
∗The DF/FF calibration has been introduced in Section 5.2.1.1.
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CHAPTER 7. PRACTICAL ASPECTS OF IMAGE ACQUISITION 133
mulative dosemeter tends to result in ghosting (Section 7.3.4.2) and missing frames∗
[Chang and Ling 2003] problems, which overestimate and underestimate dose delivery
respectively. Such limitations are not surprising since EPIDs are generally designed
to measure transient dose distributions, not cumulative doses.
The author therefore proposes an alternative imaging sequence, where strategically-
timed image acquisition verifies both the multileaf collimator (MLC) leaf positioning
as well as the exposure duration (thereby accomplishing both geometric and dosimet-
ric verifications), while avoiding the problems discussed in the previous paragraph.
7.2.4.2 Rethinking Ghosts
Ghosting, memory effect and after-glow are among the terms commonly used, some-
what interchangeably, to describe increased pixel values due to a previous irradiation.
In fact this effect may be categorised into two types:
- a temporary increase in sensitivity due to a prior irradiation; or
- incomplete discharge where a reading already counted for the previous frame/
image gets counted again.
The extent of ghosting on the Elekta a-Si EPID has been thoroughly studied by
McDermott et al. [2004]. Section 7.3.4.2 will show:
- a quantitative example of ghosting on the Varian a-Si EPID, where a maximum
open field was imaged 75 seconds after imaging a 5 cm × 5 cm field. A shorter
∗Frame acquisition is temporarily suspended each time data transfer for clearing the buffer occurs.
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CHAPTER 7. PRACTICAL ASPECTS OF IMAGE ACQUISITION 134
delay was difficult to obtain since time was required for changing the field size;
and
- a qualitative example of ghosting on the Varian SLIC EPID, where successive
images were acquired during a step-and-shoot∗ IMRT beam.
Whereas ghosting is often regarded as a problem, the author proposes a rethink.
In fact, images may be interpreted by incorporating both spatial and temporal infor-
mation, based on the fact that:
- a portal image contains information about both the past and the present; and
- each image is formed by row-by-row readout or scanning, as opposed to instan-
taneous snapshots in film-based cameras.
These ideas will be expanded in detail in Section 7.3.4.2.
7.3 Results & Discussion
7.3.1 The SLIC: Variation with Gantry Angles
7.3.1.1 Angular Dependence of Images
When we examined the variation of the central axis pixel value (Cγ) with gantry
angle, a steady increase up to 1.5% was found as the gantry angle approached 180◦
(Figure 7.4). 2D images (Iγ) varied significantly with gantry angle. Such artefacts
∗In a step-and-shoot radiation delivery, leaves do not move while the beam is on. Beamletsor segments depicted in Figure 1.2 are delivered discontinuously; the beam is switched off duringtransition from one beamlet to the next to allow rearrangement of leaves.
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CHAPTER 7. PRACTICAL ASPECTS OF IMAGE ACQUISITION 135
0 60 120 180 240 300 360gantry (degrees)
0.99
1.00
1.01
1.02
pixel value (normalised) ∆30
∆10
Figure 7.4: Variation of Cγ (normalised to C0) with gantry angle, shown for datasets 410
and 430 (as defined in Section 7.2.1).
were most evident around regions of gantry angles 90◦ and 270◦. Pixel values differed
from C0 by up to 5%. The artefacts were visible as alternate dark and bright oval
areas on an image (Figure 7.1). Location of the dark and bright oval areas was
reversed on images between 90◦ and 270◦.
When compared pixel-to-pixel using Equation (7.1), I0 was reproducible within
2% when returned to position after gantry rotation(s). Effects from liquid settling
were well below 2%. I90 and I270 were reproducible within 2% after successive gantry
rotations.
7.3.1.2 Backscatter from Surroundings
Results from MC simulation with and without the floor structure differed by a maxi-
mum of 3% within the field. These differences were wholly attributable to statistical
uncertainty in the simulations.
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CHAPTER 7. PRACTICAL ASPECTS OF IMAGE ACQUISITION 136
7.3.1.3 Reproducibility
Figure 7.5 shows the cumulative histograms for D calculated using Equation (7.1):
1. I0 data from four sessions were compared pixel to pixel. Direct comparison
found differences up to 5%. Temperature dependence could be a contributing
factor, since a 1% change in detector response per ◦C may be expected [Louwe
et al. 2004]. When each image was normalised to C0 of the respective session,
reproducibility was well within 2%.
0 0.01 0.02 0.03 0.04 0.05difference (fraction)
population (normalised)
not normalisednormalised
0 0.01 0.02difference (fraction)
0.0
0.2
0.4
0.6
0.8
1.0
Figure 7.5: Cumulative histograms of D. Left: reproducibility of I0 with and withoutnormalisation to C0 of the respective session. Right: reproducibility of images at every 30◦
gantry angle.
2. Reproducibility of images at every 30◦ gantry angle was checked by comparing
respective images from 410 and 430. Agreement was within 2% (Figure 7.5).
7.3.1.4 Angular Correction Function
Nonlinear regression using SPSS yielded the coefficients A=-0.1603 cm−1, B=2.640,
C=-0.07938 cm−1, D=3.041, E=0.01767 degrees−1, F=.01942 degrees−1, H=1.239,
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CHAPTER 7. PRACTICAL ASPECTS OF IMAGE ACQUISITION 137
I=-0.01973, J=.005706 and K=0.9921. The square of the correlation coefficient was
0.8 i.e. the regression model successfully described 80% of the variation in the depen-
dent variable.
7.3.1.5 Comparison with Existing Techniques
Images corrected using independent techniques (gantry-dependent FF, profile averag-
ing and sinusoidal modulation) were calculated for uniformity using Equation (5.1).
Standard deviations of uniformity were 0.0081, 0.0061 and 0.0054 respectively. The
sinusoidal modulation technique developed herein was found to be the most effective
(Figure 7.6).
0.99 1 1.01 1.02 1.03difference (fraction)
0.00
0.01
0.02
0.03
0.04
population (normalised) sinusoidal modulation
profile averaginggantry-dependent FF
Figure 7.6: Histograms of uniformity to compare results of the sinusoidal modulationtechnique developed herein with existing techniques.
Image correction was repeated with reduced angular sampling of input images for
coefficient derivation. For 30◦ sampling, standard deviations of uniformity remained
unchanged. For 90◦ sampling, the standard deviations deteriorated to 0.0064 and
0.0059 for the second and third techniques respectively.
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CHAPTER 7. PRACTICAL ASPECTS OF IMAGE ACQUISITION 138
7.3.1.6 Application of the New Technique
Analysis of profiles before and after applying the sinusoidal modulation correction
showed successful application on images of a 10 cm × 10 cm beam. Figure 7.7 shows
the root-mean-square of the difference between each pixel value and its counterpart
over the opposite side of the CAX. The difference for corrected images was under
0.5%.
0 60 120 180 240 300 360gantry (degrees)
0.000
0.005
0.010
0.015
0.020
rms (fraction)
beforeafter
Figure 7.7: Root-mean-square of the difference between pixels from opposing sides of theprofile.
7.3.2 The a-Si: an Artefact in the IMRT Acquisition Mode
Figure 7.8 shows an image with the associated profiles of a large open field acquired
with the a-Si EPID. Systematic grayscale non-uniformity is obvious in both vertical
and horizontal directions, where grayscale values differed by 2% – this is clearly not an
image one would expect from a uniform beam. The anomaly was similarly observed
at both Virginia Commonwealth University and Royal Marsden Hospital, ruling out
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CHAPTER 7. PRACTICAL ASPECTS OF IMAGE ACQUISITION 139
installation-dependent factors.
0.94
0.96
0.98
1
1.02
0 10 20 300.96
0.98
1
1.02
position (cm)
0 10 20 30 400.98
0.99
1
1.01
position (cm)
Figure 7.8: The IMRT mode on the aS500: an image and corresponding profiles of alarge, uniform, open field. Pixel values (normalised to the value at CAX) differ by over2%. DF/FF calibration was done with 60 frames; the image was acquired with 835 frames,corresponding to 400 MU.
Except when the same exposure duration was used for both DF/FF calibration
and image acquisition, the anomaly was found in all the acquired images. Therefore,
the use of the aS500 as an integrating dosemeter failed a basic test. If the device
can’t handle a square, uniform, static open field – there is no reason to believe it
to be capable of handling irregular, intensity-modulated, dynamic fields. Although
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CHAPTER 7. PRACTICAL ASPECTS OF IMAGE ACQUISITION 140
there have been reports claiming success in the latter (without testing the former),
e.g. van Esch et al. [2004], the author’s understanding is that the anomalies must
have been lost in the complexity tested, hence undetected. This problem has been
reported to the EPID community [Chin and Lewis 2004].
The anomaly, which disappeared when the standard mode was used, is suspected
to be effects of interplaying factors from processes such as readout, blanking and
synchronisation. Private communication with the manufacturer suggested that the
non-instantaneous, transistor-like discharge characteristics of the detector could be
the cause.
7.3.3 The a-Si: Variation with Gantry Angles
When the images acquired at rotated gantry angles were examined, artefacts in the
form of circular rings were visible. This was most evident at gantry angle 180◦
(Figure 7.9), where grayscale values on the “peaks” and “valleys” in the image differed
by over 2%. This was once again observed at both Virginia Commonwealth University
and Royal Marsden Hospital, ruling out individual installation-dependent factors.
After returning the gantry to angle 0◦ after the rotations, the image at gantry
angle 0◦ could not be reproduced. Circular rings similar to that shown in Figure 7.9
were again visible. This raises concerns because it implies that for dosimetric work,
one should not only avoid interpreting images acquired at non-zero gantry angles, but
also images acquired at gantry angle 0◦ after gantry rotation(s). This is difficult in
practice since almost all treatments involve gantry rotation(s).
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CHAPTER 7. PRACTICAL ASPECTS OF IMAGE ACQUISITION 141
The variation is not believed to be due to changes in detector response. It is
believed to be due to displacements from calibration-time alignment of the EPID to
the beam, causing the fluence incident on the detector to change. Circular features
on Figure 7.9, which correspond to the profile of a flattening filter∗, suggest that the
apparent position of the flattening filter (with respect to the EPID) during imaging
has been shifted from that during flood field calibration.
The shift is believed to be due to non-rigidity of the EPID support arm. As the
gantry was rotated, the EPID was found to shift in vertical, longitudinal and lati-
tudinal directions. An image acquired after a deliberate shift was found to resemble
Figure 7.9 qualitatively and quantitatively.
7.3.4 Ideas for IMRT Verification
7.3.4.1 An Alternative Imaging Sequence
The alternative imaging sequence proposed by the author is explained in Figure 7.10.
Prior to irradiation and image acquisition, a sequence template would be programmed
according to the treatment plan. The sequence template would then trigger an image
acquisition at expected start and end of each segment. These are the vulnerable points
where leaf transition takes place and where errors are likely to occur. Placement of
checkpoints in this way would detect any premature or delayed transition.
For each segment, if we denote MTPS, Iα and Iω respectively as the dose map
expected based on data from the treatment planning system, the image at the begin-
∗The flattening filter has been introduced in Section 3.4.
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CHAPTER 7. PRACTICAL ASPECTS OF IMAGE ACQUISITION 142
0.92
0.94
0.96
0.98
1
0 10 20 30 40
0.96
0.98
1
position (cm)
0 10 20 300.96
0.98
1
position (cm)
Figure 7.9: An a-Si portal image, and corresponding profiles, acquired at gantry angle180◦. Pixel values have been normalised to the value at CAX.
ning of the segment and the image at the end of the segment; Tα and Tω respectively
as the time at the beginning and the time at the end of the segment, the logic for
analysis would be:
- if Iα = Iω = MTPS, delivery of the segment was correct geometrically between
Tα and Tω.
- else, if Iα = MTPS but Iω 6= MTPS, the segment finished too early;
- else, if Iα 6= MTPS but Iω = MTPS, the segment started too late;
- else, if Iα 6= MTPS and Iω 6= MTPS, the segment fails both geometric and dosi-
metric verifications.
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CHAPTER 7. PRACTICAL ASPECTS OF IMAGE ACQUISITION 143
time
������������������������������
������������������������������
������������������������������
������������������������������
�����������������������������������
�����������������������������������
������������������������������
������������������������������
DATA PULSE
IMRT MODE
BEAM S1 S2 S3 S4
DATA PULSE
LOOP 1
DATA PULSE
LOOP 2
DATA PULSE
PROPOSED SEQUENCE
Figure 7.10: Proposed imaging sequence for verifying a step-and-shoot beam. Shown is abeam consisting 4 segments (S1 to S4).
The analysis assumes constant linac output and static leaves during each segment.
For pre-treatment verification, to avoid successive image acquisition being timed too
closely together (shorter than the EPID frame-rate or shorter than the ghost recovery
period), beam irradiation may be repeated over several loops of image acquisition. In
other words, to avoid the frame-rate limit or ghosting, whenever there are two closely-
timed images, they may be separated into different loops. An example is shown in
the lower panel of Figure 7.10, where 2 loops, adding up to the complete proposed
sequence, were suggested.
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CHAPTER 7. PRACTICAL ASPECTS OF IMAGE ACQUISITION 144
7.3.4.2 Rethinking Ghosts
Figure 7.11 shows a quantitative example of ghosting from an a-Si EPID. Ghosting
caused less than 0.3% increase in grayscale value compared to an image of the same
field but without recent irradiation.
10 20 30 40position (cm)
0.998
1.000
1.002
1.004
signal (normalised)
No ghostGhosted
Figure 7.11: Profiles from a-Si portal images: with and without ghosting.
Figure 7.12 shows some images acquired with a SLIC EPID during a step-and-
shoot beam. Generally, these are the 4 categories of images one can expect from
repeated image acquisitions during a step-and-shoot beam:
1. during segment: the beam was on throughout image acquisition;
2. end of segment: the beam was on when image acquisition started, but went off
before image acquisition completes;
3. between segments: the beam was off (to allow rearrangement of leaves) through-
out image acquisition;
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CHAPTER 7. PRACTICAL ASPECTS OF IMAGE ACQUISITION 145
BETWEEN START OFEND OFDURING
SEGMENT SEGMENT SEGMENTS SEGMENT
Figure 7.12: Series of images acquired on a SLIC EPID during a step-and-shoot IMRTbeam. Images may be grouped into 4 categories: images acquired during beam-on, imagesacquired during the finishing of a segment, images acquired between two segments andimages acquired during the start of a segment.
4. start of segment: the beam was off when image acquisition started, but went
on before image acquisition completes.
The portal image on Figure 7.13 is an example from the last category. While such
an image could conveniently be dismissed as “spoilt”, it is worth a closer look. If we
interpret a portal image as consecutive rows scanned one after another (Figure 7.14),
it would be obvious that it is possible to reconstruct each row as a function of time.
Every portal image, therefore, contains not only 2D spatial information, but also
temporal information. Applying this consideration to Figure 7.13 and looking at the
rows on the image as a function of time, it can be seen that:
- during the time when the top rows were read out, the beam for the first segment
had gone off.
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CHAPTER 7. PRACTICAL ASPECTS OF IMAGE ACQUISITION 146
- at the time when the row marked “as readout reaches this row” was read out,
the beam for the 2nd segment came on. This beam was still on at the time
when the final row was read out.
Let us name the rows above the row marked “as readout reaches this row” as part A;
and the rows below it as part B of the image. Now, looking at the rows as a function
of space, it can be seen that:
- in part A, the field shape of the 1st segment is still visible although the beam
for this segment had finished – this is a ghost.
- in part B, the grayscale indicates leaf leakage, but this location is not where the
field of the 2nd segment is. The field of the 2nd segment could not be seen on
the image because it was, in fact, located at the upper portion of the image.
7.4 Conclusion
Gantry-dependent artefacts in the SLIC EPID can compromise accurate dosimetry.
The correction technique based on sinusoidal modulation detailed herein was able to
correct for artefacts
- in both dimensions of an image.
- over a continuous range of gantry angles.
- over time, without having to regenerate correction coefficients.
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CHAPTER 7. PRACTICAL ASPECTS OF IMAGE ACQUISITION 147
Figure 7.13: An image acquired on a SLIC EPID during transition from a segment to thenext. The single image registered information about the preceding segment, the transition,and also the next segment. Ghosting is visible in the history area of the image.
- without intervening in image acquisition protocols, e.g. extra image calibration.
It is a post-acquisition process independent of image acquisition.
It restores flatness to well within 2%, comparing favourably to two existing correction
techniques which are based on gantry-dependent flood field and profile averaging
respectively. Overcoming these artefacts should improve usage of the EPID in general,
not only in dosimetric applications but also in imaging, where an image free of low
frequency variations can be “windowed” more readily.
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CHAPTER 7. PRACTICAL ASPECTS OF IMAGE ACQUISITION 148
OF TIME
FUNCTIONROW−BY−ROW
SCANNING
Figure 7.14: Row-by-row scanning makes it possible to reconstruct each row as a functionof time.
Artefacts in the IMRT mode of the Varian aS500 EPID led to significant inaccu-
racies (over 2%) in dose quantification. The device is therefore not recommended for
IMRT dose verification until further acquisition software developments are forthcom-
ing.
The proposed alternative imaging sequence and the idea of spatial-cum-temporal
interpretation of portal images are potentially applicable for both the SLIC and the
a-Si EPIDs. Implementation of these are beyond the timescale of this thesis and
therefore await further work and development.
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Chapter 8
HIGH THROUGHPUT
COMPUTING
If the solution for treatment verification presented in Chapter 5 is to accomplish its
mission to become a clinical routine, the run time of Monte Carlo (MC) simulations
has to be clinically acceptable. On an average personal computer processor of today,
MC simulation of a typical case for treatment verification may take weeks of run time
– which is clinically unfeasible. This chapter describes the implementation of High
Throughput Computing∗ (HTC), which allows different particle histories to be run on
different processors simultaneously. Several levels of implementation will be reported
– from the Beowulf† cluster to the UK National Grid Service (NGS), which is part of
the UK e-Science‡ program.
Chapter 5 presented a MC portal dosimetry solution that is accurate and ver-
satile. This chapter contributes the speed factor.
∗High Throughput Computing has been introduced in Section 1.6.†Beowulf is a project for combining independent computers through software and networking.
The website is at www.beowulf.org.‡e-Science has been introduced in Section 1.4.
149
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CHAPTER 8. HIGH THROUGHPUT COMPUTING 150
8.1 Introduction
With increasing demands of complex radiotherapy modalities, case-by-case full MC
simulation is becoming essential for highest attainable accuracy. Therefore, the need
for MC simulation is expanding from the research domain into daily clinical routines.
Due to prohibitively long run times, however, clinical implementation is currently
limited.
Possible ways to increase the efficiency (i.e. to reduce the run time required to
achieve a given statistical uncertainty) of MC simulations include:
- variance reduction techniques∗, which introduce non-analog and/or preferential
sampling;
- denoising [Kawrakow 2002, Miao et al. 2003], which smooths noisy data as a
post-simulation process;
- HTC, which runs different particle histories simultaneously on different com-
puters. Grounded on the inherent independence of one radiation history from
another, this promises the most accurate outcome since it biases neither the
physics nor the statistics.
HTC is the subject of this chapter. Whereas it is commonly practised using cluster
computing [Love et al. 2000], a larger resource pool is available on the Grid†. The
idea of the Grid is to provide computing power in a way analogous to electrical power
∗Variance reduction techniques have been introduced in Section 3.3.†The Grid has been introduced in Section 1.4
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CHAPTER 8. HIGH THROUGHPUT COMPUTING 151
grids: the consumer plugs in whenever service is required, without necessarily being
aware of where or how the resource is generated.
8.2 Materials & Methods
8.2.1 Four Levels of Implementation
We implemented HTC at 4 levels.
1. A Beowulf cluster at the University of Surrey, which has been in operation since
year 1999 [Love et al. 2000]. A Beowulf cluster is built from Commodity Off-
The-Shelf (COTS) hardware – it is a group of cheap personal computers running
on a cheap operating system (e.g. Linux∗), connected by standard networking
(e.g. Ethernet†).
2. A pool consisting 64 SGI‡ processors at the Welsh e-Science Centre (WeSC).
This is not Beowulf since it is built from high-end servers connected by propri-
etary networking infrastructure, running a proprietary operating system (IRIX§).
3. A pool consisting over 500 desktop computers at the University of Cardiff.
These processors are not dedicated to HTC but since they are not constantly in
∗Linux is a free Unix-type operating system originally created by Linus Torvalds with contribu-tions from developers around the world. The source code is freely available to everyone.
†Ethernet is a technology that interconnects computers into a high-speed network originally de-veloped by Xerox Corporation. It is widely used because it can network a wide variety of computers,it is not proprietary, and components are widely available from many commercial sources.
‡Silicon Graphics website is at www.sgi.com.§The IRIX operating system is a technical high-performance 64-bit operating system based on
industry-standard UNIX
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CHAPTER 8. HIGH THROUGHPUT COMPUTING 152
use, their “idle times” (e.g. evenings and weekends) may be tapped for intensive
computations e.g. MC simulations.
4. The NGS: the core production-level Grid created under the UK e-Science pro-
gram. The NGS currently provides access to 168 dedicated dual 3.06 GHz Intel
Xeon processors (336 in total) spread over four UK sites.
Neither cluster- nor Grid-computing is as straightforward as “plug-and-play”.
Implementations require considerable effort. Some details will be discussed in Sec-
tion 8.3.1. The gain in run times of the simulations presented in Section 5.2.3 will be
reported.
8.2.2 Simulations on Multiple Platforms
Multi-platform versions of EGSnrc and BEAMnrc were released in December 2003
and January 2005 respectively. With the new releases, the codes now work not
only on Linux/Unix but also Windows NT/2000/XP and, with some restrictions,
even Apple Mac OSX. Among the implementations listed in Section 8.2.1, operation
systems differ: the cluster at Surrey and the NGS are both Linux-based, WeSC is
IRIX, whereas the pool at Cardiff is Windows-XP. The architectures differ too: e.g.
the processors at Surrey are Intels, whereas the ones at the WeSC are SGIs. If a
simulation is to be distributed across heterogeneous systems, several issues require
special handling, which will be discussed in Section 8.3.2.
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CHAPTER 8. HIGH THROUGHPUT COMPUTING 153
8.2.3 Planning of Simulations
Radiotherapy MC simulations often involve multiple stages, e.g. a BEAMnrc sim-
ulation of the linac head, whose output would be used as input for subsequent
DOSXYZnrc simulations of the patient and the electronic portal imaging device
(EPID). In such multiple-staged simulations, good planning saves both execution
and data transfer time. An example will be given in Section 8.3.3.
8.2.4 Simulations without Pre-installation
Installation of EGSnrc, BEAMnrc and DOSXYZnrc code systems on each and every
executing node∗ is not always feasible, especially on non-dedicated systems, because
- it might not be known beforehand which node would be free;
- period of node availability might be too short for code installation;
- disk space in the node might be limited (code installation requires over 160
megabytes);
- automated, non-interactive code installations are not always successful; and
- non-automated installation is labour-intensive and time-consuming.
A standalone, “light-weight” (i.e. small-size in terms of disk space) data shipment is
therefore necessary for running simulations without prior code installation. This data
is to be transferred to each executing node as and when a node becomes available for
running simulations.
∗A node is an individual processor from a cluster or pool consisting many processors.
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CHAPTER 8. HIGH THROUGHPUT COMPUTING 154
8.3 Results & Discussion
8.3.1 Four Levels of Implementation
Distributing a simulation across multiple nodes saves computation time. However,
without supporting software, the human labour required can be formidable. Dis-
tributing a simulation across n processors entails:
1. generating n input files, instead of one;
2. logging into each of the n nodes;
3. checking which nodes are free and which are not;
4. starting a job∗ on each of the n nodes;
5. checking which jobs have been successful and which have not been;
6. repeating steps 2 to 5 for each job which has not been successful; and
7. combining n output files.
As an improvement from the preliminary cluster setup at Surrey, we installed
Condor [Foster and Kesselman 2003] as the resource broker†, which automates steps
2 to 6. Shell scripts were also written to handle steps 1 and 7, and also to automate
interfacing between these scripts and Condor.
∗A job refers to the nth division of a simulation, which has been divided for simultaneous com-putation on different nodes.
†A resource broker matches the available resources to the user’s requests by providing a uniforminterface to access any of the available and appropriate resources.
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CHAPTER 8. HIGH THROUGHPUT COMPUTING 155
On the WeSC pool, we enabled both Condor/G and Nimrod/G resource brokers
[Foster and Kesselman 2003], so that the author has the choice of submitting jobs
remotely from Velindre Cancer Centre without having to login to WeSC. A set of
utility functions was written using the Perl programming language [Christiansen and
Torkington 2003]. Further details are given in Chin et al. [2004a]. The idea was to
accomplish the entire simulation with minimal user intervention – the user issues a
single command from a local desktop and no further user intervention is required.
Outputs are delivered direct to the local desktop at Velindre Cancer Centre once the
simulation is complete.
Condor was also used to harness idle computing resources from the non-dedicated
pool at Cardiff University. Condor is highly configurable, e.g. it can be configured
to start a job only when the keyboard has not been used for a specified period of
time (as a signal that the owner is not using the computer), and to stop the job once
a keystroke has been detected (as a signal that the owner has returned to use the
computer). In this way, the computer’s availability to its owner is unaffected.
The NGS uses Grid middleware∗ (the Globus Toolkit) to provide secure remote
access to a collection of hardware, software and support resources available to the UK
academic community. Globus also hides some system heterogeneity, such as the use
of different batch queue systems (e.g. Condor or PBSPro) to queue and start jobs
[Foster and Kesselman 2003]. Authentication is performed using digital certificates†
issued by the UK e-Science Certificate Authority.
∗Middleware connects otherwise separate applications and passes data between them.†Digital certificates provide the electronic means of establishing the user’s credentials when mak-
ing transactions on the Web.
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CHAPTER 8. HIGH THROUGHPUT COMPUTING 156
The simulations described in Section 5.2.3 were accomplished on the NGS. Nim-
rod/G was used as a high-level tool to create and monitor individual jobs, and as a
resource broker to choose on which resources jobs should run [Abramson et al. 2000].
The geometry contained 75×75×109 voxels. The incident beam was 15 cm × 15 cm.
Tally voxels, each of 0.08 cm × 0.5 cm × 3.0 cm, achieved 1% uncertainty in the
penumbra and 0.4% in the beam. This simulation would have taken 6 days to run
on a single 2.66 GHz Intel Pentium 4 processor. Using the NGS, and in competition
with other users’ computations, the DOSXYZnrc simulation took less than 3 hours
to complete. This 50-fold increase in simulation efficiency brings the run time much
closer to an acceptable time frame for clinical operation.
8.3.2 Simulations on Multiple Platforms
The Perl utility functions developed herein are portable across different platforms,
“light-weight”, and do not require compilation. These scripts are transferred along
with each job submission. When a job finishes, the appropriate functions are auto-
matically called to convert output files from binary format (which is architecture-
dependent) into text format (which is architecture independent). Text versions of the
output files are then transferred back to the user’s local desktop computer, which will
be able to understand all the output files that are transferred back regardless of the
architecture used to compute each job.
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CHAPTER 8. HIGH THROUGHPUT COMPUTING 157
8.3.3 Planning of Simulations
Figure 8.1 shows an example of how a multi-staged simulation was run on the WeSC
using Condor. Automation was complemented by the in-house Perl utility functions.
Immediately following the completion of each job (or “child simulation” in the figure),
the utility functions trigger consecutive multi-stage jobs as required, without having
to wait for sibling∗ jobs to finish. Combination of phase space files are done auto-
matically. A similar distribution scheme has been used for all levels of HTC given in
Section 8.2.1, even when using other resource brokers.
8.3.4 Simulations without Pre-installation
The “light-weight” directory tree† transferred to each executing node was as follows:
. pegs4/data/521icru.pegs4dat
. data/incoh.data
. data/nist brems.data
. data/photo relax.data
. data/msnew.data
. data/photo cs.data
. data/spinms.data
∗Siblings refer to jobs belonging to the same stage in a multi-staged simulation.†A directory tree organises data into a hierarchical structure, beginning with a root directory and
branching into subdirectories and files.
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CHAPTER 8. HIGH THROUGHPUT COMPUTING 158
Figure 8.1: A multi-staged simulation on the WeSC. .egsinp is the input file. .egslst,.3ddose and .xmgr are the output files. condor submit is a Condor command.
. mycode.exe
. mycode/mycode.io
. mycode/mycode.egsinp
where mycode is the EGSnrc code to be run. The disk space required is about 13
megabytes (compared to over 160 megabytes for a full code installation). These are
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CHAPTER 8. HIGH THROUGHPUT COMPUTING 159
relative paths∗. No absolute path is required, so that the above directory tree may be
placed anywhere, as decided by the resource broker at the time of job submission.
This has been found to work with the following command line:
mycode.exe -i mycode -p 521icru -e . -H .
which runs the code mycode by assigning mycode.egsinp as the input file, 521icru.
pegs4dat as the cross section file, and the current directory as both the user’s and the
system’s directories.
8.4 Conclusions
Migration of MC simulations from the research domain into clinical routine is no
longer impeded by formidable run times. We have not only HTC-enabled EGSnrc,
BEAMnrc and DOSXYZnrc simulations, but also developed a set of software utility
tools to automate the labour-intensive task of splitting a simulation into parallel runs.
The different levels of HTC explored, enabled and optimised paved the way for
unprecedented computing power. Each level entails different ranges of capital, main-
tenance and labour costs. Based on these factors, the decision to employ one of the
levels or a combination of several levels is to be made.
Our usage of the Grid has been free of charge. Collaboration with the WeSC has
been on a goodwill basis, as impetus for further funding and investment for both
parties. However, the service is expected to be charged for in the future.
∗A relative path is the designation of a file location in relation to the current working directory,as opposed to an absolute path which gives the exact location.
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Chapter 9
CONCLUSIONS
9.1 Summary
A Monte Carlo (MC) portal dosimetry solution for verifying radiotherapy photon
beams has been presented. It combines the technology of electronic portal imaging
devices (EPIDs) with the accuracy of MC simulations. With reference to the purpose
set out in the abstract, this project successfully developed a solution which is accurate
(2%) across the entire clinical range of beam size, gantry angle, beam-patient and
patient-imager separations. The accuracy is maintained for both pre-treatment and
on-treatment verifications. Implementation on various levels of High Throughput
Computing (HTC) prepares the solution for efficient clinical productivity.
With reference to the objective and context set out in Section 1.5, forward portal
dose prediction by the above solution has been shown to overcome the constraints
reported in existing techniques. Accuracy is not compromised at regions of inhomo-
geneous composition, at small and large field sizes, whether or not a patient/phantom
is in the beam. Separation of the EPID from the patient/phantom is no longer con-
strained to 80 cm and beyond.
160
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CHAPTER 9. CONCLUSIONS 161
The solution achieved combined accuracy, versatility and speed hitherto unre-
ported. It is therefore ready to answer the clinical need for verifying treatments of
individual patients at Velindre Cancer Centre. Such a need is by no means local,
however. The solution developed herein is expected to be equally applicable to other
radiotherapy centres.
Table 9.1 summarises the contributions of this research project to the scientific
and medical community.
Table 9.1: Original contributions reported in this thesis.
Context Contribution PublicationVoxel-based MC codes donot allow definition ofoblique planes which arerequired for simulation ofoblique beams (Chapter5)
A solution based on inte-grated phantoms where theeffect of beam obliquity is in-cluded using geometric trans-formations
Chin et al. [2003]
Response of the SLICEPID varies with linearaccelerator gantry angle(Chapter 7)
A correction technique basedon nonlinear regression ofa three-variable sinusoidalmodulation
Chin et al. [2004b]
Long run times of MCsimulations hinder clin-ical implementation(Chapter 8)
Implementation of BEAMnrcMC simulations on the GRID
Chin et al. [2004a]
Dosimetric use of a-SiEPIDs (Chapter 7)
Identified significant anoma-lies which could compromisedosimetric accuracy
Chin and Lewis [2004]
The need for a verifica-tion solution for photonteletherapy (Chapter 5)
A MC portal dosimetry solu-tion which has been tested un-der a wide range of clinicalconditions
Chin et al. [2005]
MC studies of radiationtransport in the a-Si andSLIC detectors (Chapter6)
Design of simplified EPIDmodels for MC simulations
in preparation
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CHAPTER 9. CONCLUSIONS 162
This work included both the scanning liquid ionisation chamber (SLIC) and the
amorphous silicon (a-Si) EPID types, with a slight emphasis on the former. This is
because an a-Si EPID was not available locally during this project; experiments on the
device were carried out at our collaborating institutions. As detailed in Section 5.4,
the MC portal dosimetry solution is expected to be readily adaptable for the a-Si
EPID. In fact, the application for the a-Si EPID should be simpler due to the linear
dose response and the absence of the bulging effect.
While some North American and European centres are replacing SLIC EPIDs
with a-Si EPIDs, the former is not becoming obsolete just yet in the wider world.
Indeed, there have already been requests for further information on our SLIC EPID
work from other countries.
9.2 Further Work
The following topics are beyond the timescale of this thesis and therefore await further
work and development:
- clinical trials using the MC portal dosimetry solution developed herein for ver-
ifying radiotherapy photon treatments at Velindre Cancer Centre;
- the alternative imaging sequence based on strategically programmed sequence
templates, as proposed in Chapter 7;
- the new way of interpreting portal images by incorporating both spatial and
temporal information as proposed in Chapter 7;
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CHAPTER 9. CONCLUSIONS 163
- MC portal dose prediction of electron beams by simulating energy deposition
by bremsstrahlung photons on the EPID; and
- feasibility studies of developing and using inverse Monte Carlo∗ simulations to
reconstruct patient dose from physically acquired portal images.
∗By inverse Monte Carlo the author refers to simulations that truly invert radiation histories,where a new code with “speeding powers” instead of “stopping powers”, and inverse solutions tovarious transport equations etc. have to be developed, as opposed to the adjoint Monte Carlo alreadyavailable in MCNP, which operates on the multigroup (rather than continuous energy) mode [Wagneret al. 1993]. Application of the latter for portal dose reconstruction has been reported by Jarry andVerhaegen [2004].
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DISSEMINATION OF WORK
Journal Publications
Chin PW, Spezi E and Lewis DG 2003 Monte Carlo simulation of portal dosime-try on a rectilinear voxel geometry: a variable gantry angle solution, Physics inMedicine & Biology 48 N231-8
Chin PW, Lewis DG and Spezi E 2004 Correction for dose-response variation ina scanning liquid ion chamber EPID as a function of linac gantry angle, Physicsin Medicine & Biology 49 N93-103
Proffered Conference Presentations with Extended
Abstracts
Chin PW, Lewis DG and Giddy J 2004 Implementation of BEAMnrc MonteCarlo simulations on the GRID, Proc 14th Int Conf on the Use of Computersin Radiation Therapy ed Yi BY, Ahn SD, Choi EK and Ha SW (Seoul: Jeong)
Chin PW and Lewis DG 2004 Monte Carlo portal dosimetry for segmentedIMRT verification using the SLIC, Proc 8th Int Workshop in Electronic PortalImaging (Brighton)
Chin PW, Lewis DG and Jarvis RJ 2004 The Varian aS500 as a dosemeter:preliminary investigations, Proc 8th Int Workshop in Electronic Portal Imaging(Brighton)
Chin PW and Lewis DG 2005 A Monte Carlo solution for external beamphoton radiotherapy verification, Monte Carlo 2005 Conference – the MonteCarlo Method: Versatility Unbounded In A Dynamic Computing World (Chat-tanooga)
177
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APPENDIX A. DISSEMINATION OF WORK 178
Proffered Conference Presentations with Short Ab-
stracts
9th Annual Monte Carlo Users Group Meeting 2003, Edinburgh
All Wales Medical Physics & Clinical Engineering Summer Meeting 2003, Bodel-wyddan
10th Annual Monte Carlo Users Group Meeting 2004, Teddington
Speaking of Science Postgraduate Conference 2004, Cardiff
Current Topics in Monte Carlo Treatment Planning 2004, Montreal
All Wales Medical Physics & Clinical Engineering Summer Meeting 2004, Cardiff
IPEM Annual Scientific Meeting 2004, York
11th Annual Monte Carlo Users Group Meeting 2005, Birmingham
Visiting Talks
2003 Virginia Commonwealth University, Richmond
2003 Royal Marsden Hospital, London